Factor 3x^4-4x^2+12x^2-16

$3 x^{4} - 4 x^{2} + 12 x^{2} - 16$

Step 1

Add $- 4 x^{2}$ and $12 x^{2}$ .

$3 x^{4} + 8 x^{2} - 16$

Step 2

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

$3 {(x^{2})}^{2} + 8 x^{2} - 16$

Step 3

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

$3 u^{2} + 8 u - 16$

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 $a \cdot c = 3 \cdot - 16 = - 48$ and whose sum is $b = 8$ .

Factor $8$ out of $8 u$ .

$3 u^{2} + 8 (u) - 16$

Rewrite $8$ as $- 4$ plus $12$

$3 u^{2} + (- 4 + 12) u - 16$

Apply the distributive property.

$3 u^{2} - 4 u + 12 u - 16$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 u^{2} - 4 u) + 12 u - 16$

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

$u (3 u - 4) + 4 (3 u - 4)$

Factor the polynomial by factoring out the greatest common factor, $3 u - 4$ .

$(3 u - 4) (u + 4)$

Step 5

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

$(3 x^{2} - 4) (x^{2} + 4)$

Factor 3x^4-4x^2+12x^2-16

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