Factor 3x^4-x^2-24

$3 x^{4} - x^{2} - 24$

Step 1

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

$3 {(x^{2})}^{2} - x^{2} - 24$

Step 2

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

$3 u^{2} - u - 24$

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 $a \cdot c = 3 \cdot - 24 = - 72$ and whose sum is $b = - 1$ .

Factor $- 1$ out of $- u$ .

$3 u^{2} - (u) - 24$

Rewrite $- 1$ as $8$ plus $- 9$

$3 u^{2} + (8 - 9) u - 24$

Apply the distributive property.

$3 u^{2} + 8 u - 9 u - 24$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 u^{2} + 8 u) - 9 u - 24$

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

$u (3 u + 8) - 3 (3 u + 8)$

Factor the polynomial by factoring out the greatest common factor, $3 u + 8$ .

$(3 u + 8) (u - 3)$

Step 4

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

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

Factor 3x^4-x^2-24

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