Question

Factorisex^3+13x^2+22x+20

Answer 1

Correct Question :

Factorise : x³ + 13x² + 32x + 20

Solution :

Let p(x) be x³ + 13x² + 32x + 20

We shall find the factors of 20 first,These are : ±1, ±2, ±4, ±5, ±10, ±20

By Hit and Trial Method :

When x = +1

→ p(1) = (1)³ + 13(1)² + 32(1) + 20

→ p(1) = 1 + 13 + 32 + 20

→ p(1) = 66

$\therefore$ (x - 1) isn't factor of p(x)

Now,When x = -1

→ p(-1) = (-1)³ + 13(-1)² + 32(-1) + 20

→ p(-1) = -1 + 13 - 32 + 20

→ p(-1) = - 33 + 33

→ p(-1) = 0

$\therefore$ (x + 1) is factor of p(x)

After dividing, (x³ + 13x² + 32x + 20) by (x + 1) We obtained quotient as (x² + 12x + 20)

(Refer to the attachment)

• x³ + 12x + 20

[Splitting Middle Term]

→ x³ + 10x + 2x + 20

→ x(x + 10) + 2(x + 10)

→ (x + 2) (x + 10)

$\therefore$ x³ + 13x² + 32x + 20 = (x + 1) (x + 2) (x + 10)