Factor by Grouping 6x^4-5x^2+12x^2-10

$6 x^{4} - 5 x^{2} + 12 x^{2} - 10$

Step 1

Add $- 5 x^{2}$ and $12 x^{2}$ .

$6 x^{4} + 7 x^{2} - 10$

Step 2

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$6 {(x^{2})}^{2} + 7 x^{2} - 10$

Step 3

Let $u = x^{2}$ . Substitute $u$ for all occurrences of $x^{2}$ .

$6 u^{2} + 7 u - 10$

Step 4

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 6 \cdot - 10 = - 60$ and whose sum is $b = 7$ .

Factor $7$ out of $7 u$ .

$6 u^{2} + 7 (u) - 10$

Rewrite $7$ as $- 5$ plus $12$

$6 u^{2} + (- 5 + 12) u - 10$

Apply the distributive property.

$6 u^{2} - 5 u + 12 u - 10$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(6 u^{2} - 5 u) + 12 u - 10$

Factor out the greatest common factor (GCF) from each group.

$u (6 u - 5) + 2 (6 u - 5)$

Factor the polynomial by factoring out the greatest common factor, $6 u - 5$ .

$(6 u - 5) (u + 2)$

Step 5

Replace all occurrences of $u$ with $x^{2}$ .

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

Factor by Grouping 6x^4-5x^2+12x^2-10

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