Question

Factorise : x

x^3
+ 6x
^2
+ 4x - 8​

Answer 1

Question

Factorize for x: x³ + 6x²  + 4x - 8​

The equation of degree 3 can be solved by factor theorem.

Rational root theorem, possible zeros are ±1, ±2, ±4, ±8(Factors of 8)

Now, let's try finding zeros.

Is zero x = - 1 ?

- 1 + 6 - 4 - 8 ≠ 0 , no.

Is a zero x = 1 ?

1 + 6 + 4 - 8 ≠ 0 , no.

Is a zero x = 2 ?

8 + 24 + 8 - 8 ≠ 0 , no.

Is a zero x = -2 ?

-8 + 24 - 8 - 8 = 0, yes.

After trying four times, we found one root x = - 2 .

Factor theorem, x + 2 is one of a factor.

(It is a division by linear polynomial. It is easier to use synthetic division here.)

x³ + 6x²  + 4x - 8​ = ( x² + 4x - 4 )( x + 2 )

Therefore, ( x² + 4x - 4 )( x + 2 ) is the factorization.