Factorize $x^{3} + 13 x^{2} + 32 x + 20$

(x - 1) (x + 2) (x + 5)

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(x + 1) (x + 2) (x - 5)

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(x - 2) (x + 3) (x + 10)

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

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Solution

The correct option is D $(x + 1) (x + 2) (x + 10)$
The value of $x^{3} + 13 x^{2} + 32 x + 20$ is
$x^{3} + x^{2} + 12 x^{2} + 12 x + 20 x + 20$
$= x^{2} (x + 1) + 12 x (x + 1) + 20 (x + 1)$
$= (x - 1) (x^{2} + 12 x + 20)$
$= (x - 1) (x^{2} + 10 x + 2 x + 20)$
$= (x + 1) [x (x + 10) + 2 (x + 10)]$
$= (x + 1) (x + 2) (x + 10)$

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Similar questions

Q. State True or False:

x^{3} + 13 x^{2} + 32 x + 20

= (x + 1) (x + 2) (x + 10)

Q. Factorise the expression

x^{3} - 6 x^{2} + 11 x - 6

Check whether the following are quadratic equations :
(i) ${(x + 1)}^{2} = 2 (x - 3)$
(ii) $x^{2} - 2 x = (- 2) (3 - x)$
(iii) $(x - 2) (x + 1) = (x - 1) (x + 3)$
(iv) $(x - 3) (2 x + 1) = x (x + 5)$
(v) $(2 x - 1) (x - 3) = (x + 5) (x - 1)$
(vi) $x^{2} + 3 x + 1 = {(x - 2)}^{2}$
(vii) ${(x + 2)}^{3} = 2 x (x^{2} - 1)$
(viii) $x^{3} - 4 x^{2} - x + 1 = {(x - 2)}^{3}$

\frac{x^{2} + 3 x + 5}{(x + 1) (x + 2) (x + 3)} =

\frac{A}{(x + 1)} + \frac{B}{(x + 1) (x + 2)} + \frac{c}{(x + 1) (x + 2) (x + 3)}

then ascending order of A, B, C is

Q. Solve for

x :

2 (x + 1) (x + 3) + 8 = (2 x + 1) (x + 5)

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Factorize x3+13x2+32x+20

The correct option is D (x+1)(x+2)(x+10)The value of x3+13x2+32x+20 isx3+x2+12x2+12x+20x+20=x2(x+1)+12x(x+1)+20(x+1)=(x−1)(x2+12x+20)=(x−1)(x2+10x+2x+20)=(x+1)[x(x+10)+2(x+10)]=(x+1)(x+2)(x+10)

Factorize $x^{3} + 13 x^{2} + 32 x + 20$