Question

In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not:
f(x) = x³-6x²-19x+84, g(x) = x-7

Answer 1

$\textbf{Concept used:}$

$\textbf{Factor theorem:}$

$\text{(x-a) is a factor of f(x) iff f(a) =0}$

$\textbf{Given:}$

$\text{f(x)=}=x^3-6x^2-19x+84$

$\text{g(x)=}x-7$

$\text{Consider,}$

$\text{f(7)}$

$=7^3-6(7)^2-19(7)+84$

$=343-294-133+84$

$=427-427$

$=0$

$\therefore\textbf{By factor theorem, g(x) is a factor of f(x)}$

Find more:

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2.Find the value is of a and b, so that (x+1) and (x-1) are factors of x⁴+ax³-3x²+2x+b.

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Answer 2

Answer:

•g(x) is factor of f(x)

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