1. For items 14-15. What is the remainder when 3x300 – 2x250 + 2x105

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khyliajaine13 @khyliajaine13

August 2022 1 4 Report

1. For items 14-15. What is the remainder when 3x300 – 2x250 + 2x105 – 7x55 - 3 is divided by
14. (x + 1)?
15.(x - 1)?

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MrFahrenheit

Verified answer

REMAINDER THEOREM

Question:

What is the remainder when $3x^{300} - 2x^{250} + 2x^{105} - 7x^{55} - 3$ is divided by:

x + 1?
x - 1?

Answer with Step-by-step explanation:

We can apply the Remainder Theorem in order to solve for the remainder of the given polynomial given its binomial divisor. If we use the long division or synthetic division, it would probably take long computation time to solve for the remainder. By using the Remainder Theorem, we can solve for the remainder of the polynomial divided by the given polynomial by just simply substituting the value of the root/zero of the divisor to the value of x of the polynomial dividend. Let us try this:

@ x+1

Equate x+1 to zero. So x = -1.

By substitution:

$3(-1)^{300} - 2(-1)^{250} + 2(-1)^{105} - 7(-1)^{55} - 3\\= 3(1) - 2(1) + 2(-1) - 7(-1) -3\\= 3 - 2 - 2 + 7 - 3\\= 3$

Therefore, the remainder is 3.

@ x-1

Equate x-1 to zero. So x = 1.

By substitution:

$3(1)^{300} - 2(1)^{250} + 2(1)^{105} - 7(1)^{55} - 3\\= 3(1) - 2(1) + 2(1) - 7(1) -3\\= 3 - 2 +2 - 7 - 3\\= -7$

Therefore, the remainder is -7.

Learn more about the remainder theorem:

brainly.ph/question/6613706

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REMAINDER THEOREM

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