Question

Factorize x³+13x²+32x+20 y factor theorem

Answer 1

Answer:

Therefore (x + 1) is a factor of p(x). Hence, x3 + 13x2 + 32x + 20 = (x + 1) (x +2) (x + 10).

Answer 2

ANSWER✔

$\sf\dashrightarrow x^3+13x^2+32x+20$

$\sf\therefore taking\: g(x)=(x+1)$

$\sf\implies x=-1$

$\sf\implies (-1)^3+13 (-1)^2+32 (-1)+20$

$\sf\implies (-1)+13+(-32)+20$

$\sf\implies 12-32+20$

$\sf\implies -20+20$

$\sf\implies 0$

$\sf\therefore\red {(x+1)\: is\: a \:factor\: of \:p(x)}$

$\sf\therefore on\: dividing \:the \: x^3+13x^2+32x+20 \:by \:g(x) = (x+1)$

WE GET,

✯NOTE:-PLEASE REFER THE ATTACHMENT.

$\sf\implies (x+1)(x^2+12x+20)$

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

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

$\sf\implies (x+1)\big(x(x+10)+2(x+10) \big)$

$\sf\implies (x+1)(x+2)(x+10)$

$\large{\boxed{\bf{ \star\:\:(x+1)(x+2)(x+10) \:\: \star}}}$

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