Factor 2x^2+9x+4

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

Step 1

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 $a \cdot c = 2 \cdot 4 = 8$ and whose sum is $b = 9$ .

Factor $9$ out of $9 x$ .

$2 x^{2} + 9 (x) + 4$

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

$2 x^{2} + (1 + 8) x + 4$

Apply the distributive property.

$2 x^{2} + 1 x + 8 x + 4$

Multiply $x$ by $1$ .

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + x) + 8 x + 4$

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

$x (2 x + 1) + 4 (2 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$(2 x + 1) (x + 4)$

Factor 2x^2+9x+4

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