How do you use the factor theorem to determine whether x-2 is a factor of $x^3 + 2x^2 - 5x - 6$ ?

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Answer 1 · 2016-09-08T02:23:13

$(x-2)$ is a factor of $x^3+2x^2-5x-6$ .

According to factor theorem if $(x-a)$ is a factor of $f(x)$ , then $f(a)=0$ .

Hence to determine whether $(x-2)$ is a factor of $x^3+2x^2-5x-6$ or not, one needs to find the value of $f(2)$ .

As $f(x)=x^3+2x^2-5x-6$ ,

$f(2)=2^3+2×2^2-5×2-6$

= $8+8-10-6$

= $0$

Hence, $(x-2)$ is a factor of $x^3+2x^2-5x-6$ .

How do you use the factor theorem to determine whether x-2 is a factor of x^3 + 2x^2 - 5x - 6x^3 + 2x^2 - 5x - 6?