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

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

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Answer 1 · 2016-09-19T08:16:23

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

Explanation:

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

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

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

= $2 \times (- 64) + 3 \times 16 - 29 \times (- 4) - 60$ $2×(-64)+3×16-29×(-4)-60$

= $- 128 + 48 + 116 - 60$ $-128+48+116-60$

= $164 - 188 = - 24$ $164-188=-24$

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

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

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