Question

Factorise x^3+13x^2+32x+20

Answer 1

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Here we have :-

p(x) = x³ - 13x² + 32x + 20

Constant = 20

Factors are 20 = ±1 , ±2 , ±4 , ±5

Hence,

p(-1) = (-1)³ + 13(-1)² + 32(-1) + 20

= -1 + 13 - 32 + 20

= 0

Therefore,

$\Large{\boxed{\sf\:{(x + 1)\;is\;factor\;of\;p(x)}}}$

Now,

x³ + 13x² + 32x + 20 = x³ + x² + 12x² + 12x + 20x + 20

= (x³ + x²) + (12x² + 12x) + (20x + 20)

= x²(x + 1) + 12x(x + 1) + 20(x + 1)

= (x + 1)(x² + 12x + 20)

= (x + 1)(x² + 2x + 10x + 20)

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

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