Question

X3.1 +13x2 + 32x - 120 ​

Answer 1

Answer:

answered

Factorise : (i) x³+13x²+32x+20.

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ARoy

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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:

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 +

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).