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

Answer:

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

Step-by-step 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)

Answer 2

Answer:

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

Step-by-step 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)