Factor 3x^4+7x^2-6

$3 x^{4} + 7 x^{2} - 6$

Step 1

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

$3 {(x^{2})}^{2} + 7 x^{2} - 6$

Step 2

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

$3 u^{2} + 7 u - 6$

Step 3

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 $a \cdot c = 3 \cdot - 6 = - 18$ and whose sum is $b = 7$ .

Factor $7$ out of $7 u$ .

$3 u^{2} + 7 (u) - 6$

Rewrite $7$ as $- 2$ plus $9$

$3 u^{2} + (- 2 + 9) u - 6$

Apply the distributive property.

$3 u^{2} - 2 u + 9 u - 6$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 u^{2} - 2 u) + 9 u - 6$

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

$u (3 u - 2) + 3 (3 u - 2)$

Factor the polynomial by factoring out the greatest common factor, $3 u - 2$ .

$(3 u - 2) (u + 3)$

Step 4

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

$(3 x^{2} - 2) (x^{2} + 3)$

Factor 3x^4+7x^2-6

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