Question

PLEASE LAWD HELP
Philip determines the remainder of -32x^23 +5x^7 -3x^4 + 6
x+1
using the remainder theorem. How does he proceed to the correct answer?

Philip evaluates the numerator of the expression when x=−1. He finds the remainder of the division to be −24.


Philip evaluates the numerator of the expression when x=−1. He finds the remainder of the division to be 30.


Philip evaluates the numerator of the expression when x=1. He finds the remainder of the division to be 30.


Philip evaluates the numerator of the expression when x=1. He finds the remainder of the division to be −24 .

Answer 1

Using the remainder theorem, the correct option is:

Philip evaluates the numerator of the expression when x=−1. He finds the remainder of the division to be 30.

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The remainder theorem states that: When a polynomial a(x) is divided by a first order polynomial b(x), with a zero at x = k, the remainder is given by a(k).

In this problem, the polynomials are:

$a(x) = -32x^{23} + 5x^7 - 3x^4 + 6$

$b(x) = x + 1$

The zero of b(x) is:

$x + 1 = 0$

$x = -1$

Thus, the remainder is:

$a(-1) = -32(-1)^{23} + 5(-1)^7 - 3(-1)^4 + 6 = 32 - 5 - 3 + 6 = 30$

Thus, the correct option is:

Philip evaluates the numerator of the expression when x=−1. He finds the remainder of the division to be 30.

A similar problem is given at https://brainly.com/question/11456067