Question

Factorise : x3—3x2 – 10x + 24​

Answer 1

Let,

The polynomial $p (x)$ be $x^{3} - 3x^{2} - 10x + 24$

$= x^{3} + (-2x^{2} - x^{2} ) + (2x - 12x) + 24$

$=(x^{3} -2x^{2} )+(-x^{2} +2x)+(-12x+24)$

$=x^{2}(x-2)-x(x-2)-12(x-2)$

$=(x-2)(x^{2}-4x+3x-12)$

$=(x-2)[x(x-4)+3(x-4)]$

$=(x-2)[(x-4)(x+3)]$

$=(x-2)(x-4)(x+3)$

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Therefore,

Factors of $x^{3} -3x^{2} -10x+24$

$= (x-2)(x-4)(x+3)$

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