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Posted in Mathematics

If a polynomial is divided by (x-a) and the remainder equals zero then (x -a) is a factor of the polynomial. true or false


The Factor theorem states that  for any polynomial f(x) if f(c)=0 then x-c is a factor of the polynomial f(x).

If any polynomial f(x) is divided by x-a and remainder is 0 that means f(a)= 0 .In other words we can say x-a is a factor of the polynomial f(x).So the statement :If a polynomial is divided by (x-a) and the remainder equals zero then (x -a) is a factor of the polynomial is True.


Related Questions

Posted in Mathematics

The binomials shown below will be multiplied to produce a quadratic trinomial. (x + p)(x + q) Which part of the trinomial will equal the sum of p and q? A. The constant term B. The coefficient of the x-term C. The degree D. The coefficient of the x2-term

I believe the correct answer from the choices listed above is option B. The part of the trinomial will equal the sum of p and q would be the coefficient term. We do it as follows:

(x + p)(x + q) 
x^2 + px + 1x +pq
x^2 + (p+q)x + pq

Hope this answers the question. Have a nice day.

Posted in Mathematics

For f(x)=2x+1 and g(x)=x^2-7, find (f-g)(x)

I hope this helps you



(f-g)(x)=2x+1-(x^2-7)



(f-g)(x)=2x+1-x^2+7


(f-g)(x)= -x^2+2x+8

Posted in Mathematics

1. Which set of ordered pairs in the form of (x,y) does not represent a function of x? (1 Point) A. (1, 1.5), (2, -1.5), (3, 1.5), (4, 1.5) B. (0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5) C. (1, 1.5), (-1, 1.5), (2, 2.5), (-2, 2.5) D. (1, 1.5), (-1, -1.5), (2, 2.5), (-2, 2.5)

Based on the given set of ordered pairs above, the set of ordered pairs in the form of (x,y) that does not represent a function of x would be option B. Why is this so? if you notice, the number 1 in the x is being repeated so this means this is not a function. Hope this answer helps.

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Posted in Mathematics

Which test point holds true for y − 2x ≤ 1? (0, 2) (-2, 4) (1, 4) (5, 0)

So in order to find the correct answer, we can just easily plug in the values to check which ordered pair matches the given inequality above. So based on my solutions, the correct answer would be the last pair. 
 y − 2x ≤ 1
0 - 2(5)
 ≤ 1
0-10  ≤ 1
-10  ≤ 1
Hope this answer helps.

Posted in Mathematics

True or false Volume can be measured in liters or cubic meters.

The correct answer of the given statement above would be TRUE. It is true that volume can be measured in liters or cubic meters. Liters and cubic meters are units used to measure volume usually related to liquid volume. Hope this answers your question. 

Posted in Mathematics

What is f(x) = 2x2 + 28x – 5 written in vertex form?

To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a(x - h)2+ k, you use the process of completing the square. We do as follows:

f(x) = 2x^2 + 28x – 5
f(x) = 2(x^2 + 14x) – 5
f(x) = 2(x^2 + 14x + 49) – 5 - 98
f(x) = 2(x + 7)^2 – 103

Hope this answers the question. Have a nice day.

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Posted in Mathematics

Given f(x)=17-x^2, what is the average rate of change in f(x) over the interval [1, 5]?

For the answer to the question above, I'll show my to solution to the answer below.
average rate of change is 
(f(5) - f(1))/(5 - 1) = 

(17 - 5^2 - (17 - 1^2))/4 = 

(17 - 25 - 17 + 1)/4 = 
So the answer for this problem is
-6
I hope my answer helped you. Feel free to ask for more questions.

Posted in Mathematics

A certain forest covers an area of 2,000 square kilometers. Suppose that each year this area decreases by 6%. What is the function that best represents the area of the forest each year and how much area remains after 12 years? Round your answer to the nearest square kilometer. Hint: Use the formula, f(x) = P(1 + r)x

For the answer to the question above, I think the formula you is wrong. The x must be in exponential form. It must look like this

f(x) = P(1 + r)^x
Now we can solve.

Given:
P = 2000
r = -0.06

f(x)  =  2000 (1 - 0.06)^x
       =  2000 (0.94)^x


         
2000 (0.94)¹² = 

2000 (0.476)  = 
The answer is 
951.8 square kilometers.
                   

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Posted in Mathematics

Which of the following statements is true of a reflection? -It is an isometry. -It slides a plane. -The transformation is done over a line of reflection. -It flips a plane about a fixed line. I-t changes the size of the figure being reflected.

I think the correct answers from the choices listed above are the first and the fourth option. The statements that are true about a reflection would be that it  is an isometry and the it flips a plane about a fixed line. reflection over a line k (notation rk) is a transformation in which each point of the original figure (pre-image) has an image that is the same distance from line k.

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Posted in Mathematics

Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Check all that apply. + 8r2s4 – 3r3s3 s5 3r4s5 –r4s6 –6rs5

Answer:

Option 2,3 and 4 are correct.

Step-by-step explanation:

To find : Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Check all that apply.

?+8r^2s^4-3r^3s^3

Solution :

The polynomials in standard form is written from higher degree to lower degree i.e. in descending order.

The given polynomial has degree 6: ?+8r^2s^4-3r^3s^3, and it can be ordered respect any of the two variables either r or s.

Adding a new term as first term needs to have degree equal or greater than 6.

1) s^5 cannot use as first term because its degree is less than 6.

2) 3r^4s^5 it can be use as degree is 9.

3r^4s^5+8r^2s^4-3r^3s^3 is the standard form.

3) -r^4s^6 it can be use as degree is 10.

-r^4s^6+8r^2s^4-3r^3s^3 is the standard form.

4) -6rs^5 it can be use as degree is 6.

-6rs^5+8r^2s^4-3r^3s^3 is the standard form.

Therefore, Option 2,3 and 4 are correct.

Posted in Mathematics

What is the range of the function f(x) = 3x2 + 6x – 9

I have a solution here however with a slight change in the equation:

 f(x)=3x^2-6x+1

My solution is:

The domain is all real numbers--there are no restrictions like a square root or variable in the denominator 

this is a U shape parabola and you want to find the bottom point, it is at the vertex 

x=-b/2a =- (-6) /2 (3) =1 
f(1) =3(1)^2 -6(1) +1 =3-6+1 =-2 
the minimum is (1, -2) 
so the range is all real numbers >= -2

By examining my solution, you could just answer the problem on your own! I hope it helps!

Posted in Mathematics

Which of the binomial is a factor of this trinomial x2-7x-44?

I hope this helps you



x^2-7x-44

x -11



x +4



(x-11)(x+4)

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Posted in Mathematics

Which is a factor of 18?

Factors of 18: 1 2 3 6 9 18

hope this helps you

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Posted in Mathematics

When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown? 2 + 7c – 4c2 – 3c + 4 –4c2 + 4c + 6 –7c2 + 10c + 6 –4c2 + 4c + 8 –7c2 + 7c + 6

Answer:

A) -4c^2 + 4c + 6

Step-by-step explanation:

The given polynomial is 2 + 7c – 4c^2 – 3c + 4

Add the like terms.

2 + 4 + 7c - 3c -4c^2

= 6 + 4c - 4c^2

Write it in a standard form

= -4c^2 + 4c + 6

Answer is A) -4c^2 + 4c + 6

Hope this will helpful.

Thank you.

Posted in Mathematics

Arrange the following polynomial into descending order for x, then interpret the degree of the 2nd term. 7x3y3 + 4 − 11x5y2 − 3x2y

For the answer to the question above,  the power of "y" doesn't influence descending order for x even if it is higher than power of x.

Unordered polynomial is 
7x3y3 + 4 - 11x5y2 - 3x2y

Polynomial in descending order  looks like this
-11x5y2 + 7x3y3 - 3x2y + 4

Degree of the second term is 5 ( because of x5 ) 

Posted in Mathematics

Which of the following is a factor of 2x4 + 22x3 + 60x2? 2x3 x4 x + 4 x + 5

The correct answer is Option D, or X+5. I hope I answered this question to your satisfaction Have a nice day!

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Posted in Mathematics

Which polynomial expression represents the area of the outermost square tile, shown below? A square shaped tile with length x plus three is shown x2 + 6x + 6 x2 + 9x + 6 x2 + 6x + 9 x2 − 6x + 9

I believe the correct answer from the choices listed above is the third option. The polynomial expression that represents the area of the outermost square tile would be x^2 + 6x + 9. The area of a square is calculated by the square of its side and the side of this square is given as x+3.

A = (x+3)^2 = x^2+6x+9

Posted in Mathematics

What is the additive inverse of the polynomial 9xy^2 + 6x^2y – 5x^3? A.9xy2 – 6x2y + 5x3 B. 9xy2 – 6x2y – 5x3 C. 9xy2 + 6x2y + 5x3 D. 9xy2 – 6x2y + 5x3

Are you sure that you wrote all your choices right?
Because for so solving the additive inverse of 9xy² + 6x²y - 5x³

-1(9xy² + 6x²y - 5x³)  then it will turn to this ⇒ (-1)(9xy²) + (-1)(6x²y) + (-1)(-5x³)

-9xy² - 6x²y + 5x³ is the additive inverse of the given polynomial.

Posted in Mathematics

What times what equals 429

20.71 * 20.71 = 429

Your answer is 20.71
If you want more than it is 20.71231517

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Posted in Mathematics

What is 22,274 divided by 37

The answer is 61.459 repeating

Posted in Mathematics

Solve for x. round to nearest tenth if needed. 1. 7r-7=2r+18 a.r=-5 b.r=5 c.r=2.2 d.r=1.2 2. 2x+12=18-x a.x=3 b.x=10 c.x=6 d.x=2 3. 8x-3=15x+18 a.x=-3 b.x=3 c.x=2.1 d.x=0.9 4. 6y-6=4y+16 a.y=2.2 b.y=-2.2 c.y=11 d.y=5 5. 3(x-4)=5(x+2) a.x=11 b.x=-11 c.x=1 d.x=-1

1)  The answer is: [B]: r = 5 .
__________________________
Explanation:
__________________________ 
Given: 7r − 7 = 2r + 18 ; Round your answer to the nearest tenth, if necessary.
____________________________
Since "r" is the only variable given, let us assume we want to solve for "r" (instead of "x").
___________________________
→ Subtract "2r" from EACH SIDE of the equation; and & add "7" to EACH SIDE of the equation:
_____________
→ 7r − 7 − 2r + 7 = 2r + 18 − 2r + 7 ;  to get: → 5r = 25 ;
_____________
→ Now, divide EACH SIDE of the equation by "5"; to isolate "r" on one side of the equation; and to solve for "r" :
______________
→ 5r / 5 = 25 / 5 → r = 5 → which is: "Answer choice: [B]".
_________________
Let us check our answer, by plugging in "5" for "r" in the original equation:
_________________
 → 7r − 7 = 2r + 18 ;  →  7(5) − 7 =? 2(5) + 18? ;
______________________
→ 35 − 7 =? 10 + 18 ?;     → 28 =? 28? Yes!
______________________
 2) The answer is: [D]: x = 2 .
_____________
Explanation: 
_____________
Given: 2x + 12 = 18 − x ; Solve for "x" (round to nearest tenth, if necessary).
_______________
→ Add "x" to EACH SIDE of the equation, & subtract "12" from EACH SIDE of the equation:  → 2x + 12 + x − 12 = 18 − x + x − 12 ; 
______________
→ To get: 3x = 6 ;  → Divide EACH SIDE of the equation by "3";
to isolate "x" on one side of the equation; and to solve for "x":
_____________
→ 3x / 3 = 6 / 3 ; → x = 2 ; which is: "Answer choice: [D]".
______________
Let us check our answer, by plugging in "2" for "x" in the original equation:
________________
→ 2x + 12 = 18 − x ; → 2(2) + 12 =? 18 − 2 ?
________________
→ 4 + 12 =? 18 − 2 ? ;   → 16 =? 16?  Yes!
________________________________
3)  The answer is: [A]: x = -3 . 
_____________
Explanation:
________________
Given:  8x − 3 = 15x + 18 ; Solve for "x". Round your answer to the nearest tenth, if necessary.
_________________
→ Subtract "8x" from EACH SIDE of the equation, & add "3" to EACH SIDE of the equation:
_______________
→ 8x − 3 − 8x + 3 = 15x + 18 − 8x + 3 ; to get:
_______________
→ 0 = 7x + 21 ; → Subtract "21" from EACH SIDE of the equation;
_______________
→ 0 − 21 = 7x + 21 − 21 ; to get:
_______________
→  -21 = 7x ; Now divide EACH SIDE of the equation by "7";
    to isolate "x" on one side of the equation; & to solve for "x":
_______________
→ = -21 / 7 = 7x / 7 ; →  -3 = x ; which is "Answer choice: [A]."
_________________
Let us check our answer, by plugging in "-3" for "x" in the original equation:
________________
→  8x − 3 = 15x + 18 ;  → 8(-3) − 3 =?  15(-3) + 18 ?;
________________________
→ -24 − 3 =?  -45 + 18 ? ;   →  -27 =? -27?  Yes!
___________________________
4)  The answer is: [C]: y = 11 .
_____________
Explanation:
____________
Given: 6y − 6 = 4y + 16 ; Solve for "y"; Round to the nearest tenth, if necessary.
____________
(Note: Since "y" is the only variable given; assume we are to solve for "y" instead of "x").
____________
→ Subtract "4y" from EACH SIDE of the equation, & add "6" to EACH SIDE of the equation; → 6y − 6 − 4y + 6 = 4y + 16 − 4y + 6 ; to get:
_______________
→ 2y  = 22 ; Now, divide EACH SIDE of the equation by "2"; to isolate "y" one side of the equation; and to solve for "y" ;
_______________
→ 2y / 2 = 22 / 2 ; →  y = 11 → which is "Answer choice: [C]".
_______________________________
Let us check our answer, by plugging in "11" for "y" in the original equation:
___________________
→  6y − 6 = 4y + 16 ; → 6(11) − 6 =? 4(11) + 16 ?
_______________________
→ 66 − 6  =? 44 + 16 ?  → 60 =? 60 ?  Yes!
__________________
5)  The answer is: [B]: x = -11 .
_____________________
Explanation:
_________________
Given: 3(x − 4) = 5(x + 2) ; Solve for "x". Round to the nearest tenth, if necessary.
___________
→Note the "distributive property of multiplication": 
_____________
a*(b + c) = ab + ac ;  and: a*(b − c) = ab − ac ;
_______________
→ Let us expand EACH SIDE of our given equation.
→Start with the "left-hand side":
____________
3(x − 4) = (3*x)  − (3*4) = 3x − 12;
______________________________
→Now let us expand the "right-hand side" of the given equation:
____________
→  5(x + 2) = (5*x) + (5*2) = 5x + 10 ;
______________
→Now, we can rewrite the original equation:
_______________
→ 3(x − 4) = 5(x + 2) ; by substituting the expanded values for EACH SIDE of the question:   →  3x − 12 = 5x + 10 ;
__________________
→ Subtract "3x" from EACH SIDE of the equation; and add "12" to EACH SIDE of the equation: →  3x − 12 − 3x + 12 = 5x + 10 − 3x + 12 ; to get:
________________
→  0 = 2x + 22;  → Now subtract "22" from EACH SIDE of the equation:
______________
→  0 − 22 = 2x + 22 − 22 ; to get:  →  -22 = 2x ;
__________
→ Divide EACH SIDE of the equation by "2"; to isolate "x" on one side of the equation; & to solve for "x" ;
_____________
→  -22 / 2 = 2x /2 ;  →  -11 = x ; which is "Answer choice: [B]".
______________
Let us check our answer, by plugging in "-11" for "x" in the original equation:
___________
→ 3(x − 4) = 5(x + 2) ; →  3(-11 − 4) =? 5(-11 + 2) ? ; 
_______________________
→3(-15) =? 5(-9) ? ; → -45 =? -45 ?  Yes!
_____________________________________________
Hope these answers and explanations are helpful. Best of luck!

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Posted in Mathematics

Calculate the moments Mx, My, and the center of mass (x bar, y bar) of a lamina with the given density p=5 and the shape:

M x = 1/2 p ∫ ( f ( x )² - g ( x )² ) d x
f ( x ) = √( 1 - x²),  g ( x ) = - 2
M x = 1/2 * 5  \int\limits^1_{-1} (- x^{2} -3)\, dx= \\ =-5/2 * [ x^{3}/3 + 3 x]^1 _{-1} = \\ =-5/2 * (1/3+3+1/3+3)=
= - 50/3
My = p ∫ x * ( f ( x ) ) dx
My = p ∫ x ( √(1+x²)) dx
Substitution: 1 - x² = u,  x dx = - du/2
M y = 5 *  \int\limits^0_0 { \sqrt{u} } \, du = 0
M x = - 50/3, M y = 0
M = 5 *  \int\limits^1_{-1}  { (\sqrt{1+ x^{2} }+2)} \, dx  = \\ 
=5* [1/2  \sqrt{1+ x^{2} }  *x + 2 x + 1/2 *sinh ^{-1} x]^1_{-1}
M ≈ 5 * 6.3 ≈ 31.2  
x = M y / M = 0 / 31.5 = 0
y = M x / M =  -50/3 : 31.5 ≈ - 0.529
The center of mass is ( 0, -0.529 )


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