Question

Assume that any variable exponents represent whole numbers. Factor the greatest common factor from the polynomial.

Answer 1

Question:

Assume that any variable exponents represent whole numbers. Factor the greatest common factor from the polynomial.

`9x^4 -6x^2`

Answer:

`3x^2(3x^2 -2)`

Explanation:

Given

`9x^4 -6x^2`

Required

Factorize

`9x^4 -6x^2`

Express 9 as 3 * 3 and 6 as 3 * 2

`3 * 3x^4 -3 * 2x^2`

Factorize 3 from both terms

`3(3x^4 -2x^2)`

Express x^4 as x^2 * x^2

`3(3x^2 * x^2 -2x^2)`

Factorize x^2 from both terms

`3x^2(3x^2 -2)`

Hence, the factors of
`9x^4 -6x^2` are

`3x^2` and
`3x^2 - 2`