Factor 8x^4+18x^2+9

$8 x^{4} + 18 x^{2} + 9$

Step 1

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

$8 {(x^{2})}^{2} + 18 x^{2} + 9$

Step 2

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

$8 u^{2} + 18 u + 9$

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 $a \cdot c = 8 \cdot 9 = 72$ and whose sum is $b = 18$ .

Factor $18$ out of $18 u$ .

$8 u^{2} + 18 (u) + 9$

Rewrite $18$ as $6$ plus $12$

$8 u^{2} + (6 + 12) u + 9$

Apply the distributive property.

$8 u^{2} + 6 u + 12 u + 9$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 u^{2} + 6 u) + 12 u + 9$

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

$2 u (4 u + 3) + 3 (4 u + 3)$

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

$(4 u + 3) (2 u + 3)$

Step 4

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

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

Factor 8x^4+18x^2+9

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