Question

factorise


${x}^{3} + 13 {x}^{2} + 32x + 20$
​

Answer 1

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

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

= -33 + 33

= 0

Hence, (x + 1) is a factor of p(x)

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)

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