Question

factorize x^3+13x^2+32x+20​

Answer 1

Answer:

Factorise :- x^3 + 13x^2 + 32x + 20 - Mathematics

As p(−1) is zero, therefore, x + 1 is a factor of this polynomial p(x). Let us find the quotient on dividing x3 + 13x2 + 32x + 20 by (x + 1).

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Answer 2

Answer:

$(x+1)(x+2)(x+10)$

Step-by-step explanation:

Let $P(x)=x^3+13x^2+32x+20$

By integer root theorem, the zeroes of P(x) must be a factor of the constant term 20

$P(-1)=(-1)^3+13(-1)^2+32(-1)+20=-1+13-32+20=0$

$\implies$ -1 is a zero of P(x)

So, $(x+1)$ is a factor of P(x)

After dividing P(x) by (x+1) by long division, we get -

$P(x)=(x+1)(x^2+12x+20)$

$\implies P(x)=(x+1)(x^2+2x+10x+20)$

$\implies P(x)=(x+1)[x(x+2)+10(x+2)]$

$\therefore P(x)=(x+1)(x+2)(x+10)$