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1. The expression x - 3 is a factor of the function p (x). What is the remainder when p (x) is divided by x - 3?

2. What will be the remainder when the polynomial p (x ) = 3x 5 - 8x 3 + 4x 2 - 41 is  divided by x - 2?

3. If the binomial (x-7) is a factor of the polynomial function f(x), which statement must be true?

A. f(7)=-7

B. f(7)=0

C. f(-7)=0

D. f(-7)=-7

 

Sorry for asking so many questions but I am trying to find the answer on my own first. I'm just really sick and my brain does not want to do math. Please help and show work. Thank you so much!

 Mar 11, 2019
 #1
avatar+99441 
+1

1.   If  x - a is a factor, then the remainder when P(x) is divided by x- a  will be 0

[ A "factor" of a polynomial means that it divides the polynomial evenly....there will be a remainder of 0 ]

 

2. What will be the remainder when the polynomial p (x ) = 3x 5 - 8x 3 + 4x 2 - 41 is  divided by x - 2?

 

If a polynomial  is divided by  x - a.....then the remainder   will =  P(a).....in other words....we put "a" into the polynomial  and evaluate.....the evaluation will be the remainder

 

So......x - a  = x -2      ....so....we put 2 into the polynomal  and we get

 

3(2)^5  - 8(2)^3  + 4(2)^2   - 41  =

 

3*32  - 8*8 + 4*4  - 41 =

 

96 - 64 + 16 - 41  =

 

7 =   the remainder

 

 

 

3. If the binomial (x-7) is a factor of the polynomial function f(x), which statement must be true?

 

If  x - a  is a factor....then "a"  is a zero....so  P(a) = 0

 

In this case.....x - 7 is a factor.....so......7 is a zero......so....P(7) = 0

 

 

cool cool  cool

 Mar 11, 2019
 #2
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Thank you so much for the help. I really appreciate your help with this!

Guest Mar 11, 2019
 #3
avatar+99441 
0

OK.....no prob.....

 

 

cool cool cool

CPhill  Mar 11, 2019

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