Question

Factorise : (i) x³+13x²+32x+20.

Answer 1

x³+13x²+32x+20
=(x+1)(x²+12x+20)   [∵, for x=-1, x³+13x²+32x+20=-1+13-32+20=0]
=(x+1)(x²+10x+2x+20)
=(x+1){x(x+10)+2(x+10)}
=(x+1){(x+10)(x+2)}
=(x+1)(x+2)(x+10)
                                                      

Answer 2

Answer:

Step-by-step explanation:Let p(x) = x3 + 13x2 + 32x + 20

p(-1) = -1 + 13 - 32 + 20 = -33 + 33 = 0

Therefore (x + 1) is a factor of p(x).

On dividing p(x) by (x + 1) we get

p(x)  (x + 1) = x2 + 12x + 20

Thus,

x3 + 13x2 + 32x + 20 = (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)

Hence, x3 + 13x2 + 32x + 20 = (x + 1) (x +2) (x + 10).