Is x+4 a factor of $2x^3+3x^2-29x-60$ ?

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Answer 1 · 2016-09-19T08:16:23

$(x+4)$ is not a factor of $f(x)=2x^3+3x^2-29x-60$

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

Here we have to test for $(x+4)$ i.e. $(x-(-4))$ . Therefore, if $f(-4)=0$ then $(x+4)$ is a factor of $f(x)=2x^3+3x^2-29x-60$ .

$f(-4)=2(-4)^3+3(-4)^2-29(-4)-60$

= $2×(-64)+3×16-29×(-4)-60$

= $-128+48+116-60$

= $164-188=-24$

Hence $(x+4)$ is not a factor of $f(x)=2x^3+3x^2-29x-60$ .

Is x+4 a factor of 2x^3+3x^2-29x-602x^3+3x^2-29x-60?