x cube + 4 x square + X - 6 factorise
Answers
Step-by-step explanation:
x^3+4x^2+x-6=(x-1)(x^2+5x+6)
=(x-1)(x+3)(x+2)
Answer:
(x - 1) (x + 3) (x + 2) is the factorised form of x³ + 4x² + x - 6.
Step-by-step explanation:
We need to factorise x³ + 4x² + x - 6
As it is a cubic equation, we will find the factors of the given equation by Hit and Trail method.
if x = 1 => 1³ + 4*1² + 1 - 6 = 1 + 4 + 1 - 6 = 0
As it satisfies the given equation, it means that x - 1 is a factor of the given equation.
=> x³ + 4x² + x - 6 = (x - 1) (x² + 5x + 6)
We will now factorise x² + 5x + 6 by mid term splitting.
=> x² + 5x + 6 = x² + 3x + 2x + 6
= x(x+3) + 2(x+3)
= (x + 3) (x + 2)
Therefore, x³ + 4x² + x - 6 = (x - 1) (x² + 5x + 6)
= (x - 1) (x + 3) (x + 2)
Therefore, (x - 1) (x + 3) (x + 2) is the factorised form of x³ + 4x² + x - 6