Question

Factorize
(i) (x^2 – 2x )^2 – 11(x^2 – 2x ) + 24
(ii) x^3 – 3x^2 – 9x – 5
(iii) x^3 + 6x^2+ 11x + 6

Answer 1

@
(1) (x²-2x)²-11(x²-2x)+24
=>Let (x²-2x) be a
= (a)²-11(a)+24
=a(a-11)+24
=a²-8a-3a + 24
=a(a-8) -3(a-8)
=(a-3)(a-8)
substitute a
=(x²-2x-3) (x²-2x-8)
splitting the middle term
=(x²-3x+x-3) (x²-4x+2x-8)
=x(x-3) + 1(x-3) * x(x-4) + 2(x-4)
=(x+1)(x-3)(x+2)(x-4)

(2) x³-3x²-9x-5
=>x²(x-3)-1(9x+5)
=(x²-1)(x-3+9x+5)
=(x²-1²)(10x+2)
=(x+1)(x-1)(5x+1)2
=2(x+1)(x-1)(5x+1)

(3) x³+6x²+11x+6
=>x³+11x+6x²+6
=x(x²+11)+6(x²+1)
=(x+6)(x²+11+x²+1)
=(x+6)(2x²+12)
=(x+6)(x²+6)(2)
=2(x+6)(x²+6)
@:-)