Factor 3y^4-2y^2-5

$3 y^{4} - 2 y^{2} - 5$

Step 1

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

$3 {(y^{2})}^{2} - 2 y^{2} - 5$

Step 2

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

$3 u^{2} - 2 u - 5$

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 $a \cdot c = 3 \cdot - 5 = - 15$ and whose sum is $b = - 2$ .

Factor $- 2$ out of $- 2 u$ .

$3 u^{2} - 2 (u) - 5$

Rewrite $- 2$ as $3$ plus $- 5$

$3 u^{2} + (3 - 5) u - 5$

Apply the distributive property.

$3 u^{2} + 3 u - 5 u - 5$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 u^{2} + 3 u) - 5 u - 5$

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

$3 u (u + 1) - 5 (u + 1)$

Factor the polynomial by factoring out the greatest common factor, $u + 1$ .

$(u + 1) (3 u - 5)$

Step 4

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

$(y^{2} + 1) (3 y^{2} - 5)$

Factor 3y^4-2y^2-5

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