Question

Factor 6x4 – 5x2 + 12x2 – 10 by grouping. What is the resulting expression?Factor 6x4 – 5x2 + 12x2 – 10 by grouping. What is the resulting expression?

Answer 1

(x^2 + 2)(6x^2 - 5)

Explanation:

Look at the first term (6x^4) and the third (12x^2). 6x^2 is common to both, as well as to the second term. We can rewrite the first and third terms as

6x^2(x^2 + 2). The second and fourth terms can be rewritten as -5(x^2 + 2). Note that (x^2 + 2) shows up as a factor twice here. We can factor (x^2 + 2) out of both terms of 6x^2(x^2 + 2) -5(x^2 + 2), obtaining:

(x^2 + 2)(6x^2 - 5)

Answer 2

`(6x^2-5)(x^2+2)`

Explanation:

In
`6x^4-5x^2+12x^2-10` we can rewrite the expression as:

`(6x^4-5x^2)+(12x^2-10)` to factor each part individually:

First in
`6x^4-5x^2` we can factor out the GCF (x²) to find:

⇒ x²(6x²-5)

And in 12x²-10 we can factor out the GCF (2) to find:

⇒ 2(6x²-5)

And we can use substitution to rewrite the orignal expression as:

⇒ x²(6x²-5)+2(6x²-5)

And in this expression the GCF is 6x²-5 and so after factoring this out we find that:

`6x^4-5x^2+12x^2-10` = (x²+2)(6x²-5)