jazzlynnlock
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The polynomial p(x) = –2x3 + 3x + 4 is given. Which conclusion is valid if P(1) = 5?
A. The remainder of p(x) divided by (x-1) is 5
B. The remainder of p(x) divided by (x-5) is 1

Sagot :

yulisaflores852
I think it’s A I hope it helps

The correct conclusion is the remainder of p(x) divided by (x-1) is 5 and this can be determined by using the factorization method.

Given :

  • [tex]\rm p(x)=-2x^3+3x+4[/tex]
  • p(1) = 5

The following steps can be used in order to determine which conclusion is correct:

Step 1 - The given expression (p(1) = 5) implies that at (x = 1) the value of p is 5.

Step 2 - According to the conclusion (A) the remainder of p(x) divided by (x-1) is 5 that is:

[tex]\rm p(x) = \dfrac{-2x^3+3x+4-5}{x-1}[/tex]

Simplify the above expression.

[tex]\rm p(x) = \dfrac{-2x^3+3x-1}{x-1}[/tex]

Now, factorize the numerator.

[tex]\rm p(x) = \dfrac{-2x^3+2x^2-2x^2+2x + x - 1}{x-1}[/tex]

[tex]\rm p(x) = \dfrac{(x-1)(-2x^2-2x+1)}{(x-1)}[/tex]

So, this conclusion is true.

Step 3 - According to the conclusion (B), the remainder of p(x) divided by (x-5) is 1 that is:

[tex]\rm p(x) = \dfrac{-2x^3+3x+4-1}{x-1}[/tex]

The numerator does not factorize. Therefore, this conclusion is false.

For more information, refer to the link given below:

https://brainly.com/question/17822016

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