When g(x) is divided by x + 4 the remainder is 0. Given g(x)=x^4+3x^3-6x+8 which conclusion about g(x) is true?

check your textbook on the Remainder Theorem.

any divisor that yields a remainder of 0 from the dividend, IS a factor of the dividend.

namely, if x⁴+3x³-6x+8 ÷ x+4, gives a remainder of 0, then x+4 IS a factor of x⁴+3x³-6x+8.

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adioabiola adioabiola · Answer 2 · 2021-10-22T12:32:06+02:00

The conclusion which is true of g(x) is therefore: (x-4) is a factor of the polynomial, g(x) = x⁴+3x³-6x+8

According to the question;

When g(x) is divided by x + 4 the remainder is 0.

However, given g(x)=x⁴+3x³-6x+8

By the Remainder theorem;

P(x) = (quotient)×divisor + Remainder.

However, when Remainder = 0.

The Divisor is a said to be a factor of the polynomial P(x).

In this scenario; the conclusion which is true of g(x) is therefore;

(x-4) is a factor of the polynomial, g(x) = x⁴+3x³-6x+8