Factorise x³+13x²+32x+20
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30
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)
=(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)
Answered by
15
x^3+13x^2+32x+20= x^3 + x^2+ 12x^2 + 12x + 20x + 20
=x^2(x+1) + 12x(x+1) +20(x+1)
=(x^2 + 12x + 20)(x+1)
=(x^2 + 10x + 2x + 20)(x + 1)
={x(x + 10) + 2(x + 10)}(x + 1)
=(x+1)(x+2)(x+10)
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