Question

Factorise:
x³+6(x+1)²-x

Answer 1

hey.. here is ur answer
x^3+6(x+1)^2-x
x^3+6(x^2+1+2x)-x ........ [by using (a+b)^2=a^2+b^2+2ab]
x^3+6x^2+6+12x-x
x^3+6x^2+11x+6
let x be -1
(-1)^3+6(-1)^2+11(-1)+6
-1+6-11+6
-12+12=0
first factor is (x+1). [as (x+1)=0
x=-1]
now divide the polynomial with (x-1)
after long division answer will be
x^2+5x+6
now by spillting the middle term
x^2+2x+3x+6
x(x+2)+3(x+2)
(x+3)(x+2)

so factors are (x+1),(x+2), and (x-3)
hope this helps