Question

1) Factorize : x3 + 13x2 + 32x + 20

2) Factorize : 8x3 + y3 + 27z3 – 18xyz.​

Answer 1

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)

2)8x 3+y 3+27z3−18xyz

using the formula, a 3 +b 3+c−3abc=(a+b+c)(a2+b2+c2 −ab−bc−ac)

=(2x) 3 +y 3+(3z) 3 −3×2x×y×3z

(2x+y+3z)[(2x) 2 +y 2 +(3z) 2−2x×y−y×3z−3z×2x]

(2x+y+3z)(4x2+y2+9z2−2xy−3yz−6zx)

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