How do you factor $x^{3} - 4 x^{2} - 11 x + 30$ $x^3-4x^2-11x+30$ ?

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Answer 1 · 2018-04-16T09:12:07

$\Rightarrow p (x) = (x - 2) (x - 5) (x + 3)$ $=>p(x)=(x-2)(x-5)(x+3)$

Here,

$p (x) = x^{3} - 4 x^{2} - 11 x + 30$ $p(x)=x^3-4x^2-11x+30$

For $x = 2$ $x=2$ ,

$p (2) = 2^{3} - 4 {(2)}^{2} - 11 (2) + 30 = 8 - 16 - 22 + 30 = 0$ $p(2)=2^3-4(2)^2-11(2)+30=8-16-22+30=0$

$\Rightarrow (x - 2)$ $=>(x-2)$ , is a factor.

$:.p(x)=x^3-2x^2-2x^2+4x-15x+30$

$=>p(x)=x^2color(green)((x-2))-2xcolor(green)((x-2))-15color(green)((x-2))$

$=>p(x)=(x-2)(x^2color(red)(-2x)-15)$

$=>p(x)=(x-2)[x^2color(red)(-5x+3x)-15]$

$=>p(x)=(x-2)[xcolor(blue)((x-5))+3color(blue)((x-5))]$

$=>p(x)=(x-2)(x-5)(x+3)$

How do you factor x^3-4x^2-11x+30x3−4x2−11x+30x^3-4x^2-11x+30?