Question

Use the remainder theorem to determine whether x=-4 is a solution of x^6+5x^5+5^4+5^3+2x^2-10x-8.​​

Answer 1

Hello haohaoxNienie!

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

Use the remainder theorem to determine whether x = - 4 is a solution of x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8.

$\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}$

Refer to the attached picture.

Steps :-

1. First find the divisor using the given information (x = - 4).
2. Now, divide x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8 by x + 4.
3. We'll get the remainder as 0.
4. Using the remainder theorem & solving it, we'll get LHS & RHS as 0.
5. Hence proved.

Answer :- Yes, x = - 4 is a solution of x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8.

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Hope it'll help you!

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