Question

factorise x cube + 13 x square + 32 X + 20 by using factor theorem

Answer 1

$\large{\boxed{\bold{Answer:}}}$

Let p(x) = x³+13x²+32x+20

By trial, we find that

$p( - 1) = ( - 1 {)}^{3} + 13( - 1 {)}^{2} + 32( - 1) + 20 \\ \\ = - 1 + 13 - 32 + 20 = 0$
By factor theorem, x-(-1) i, e(x+1) is a factor of p(x)

Now,

${x}^{3} + 13x + 32x + 20 \\ \\ = {x}^{2}(x + 1) + 12x(x + 1) + 20(x + 1) \\ \\ = (x + 1)( {x}^{2} + 12x + 20) \\ \\ = (x + 1)( {x}^{2} + 2x + 10x + 20) \\ \\ = (x + 1)(x(x + 2) + 10(x + 2) \\ \\ = (x + 1)(x + 2)(x + 10)$

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Answer 2

Please check the attached