Factor 15x^2+16x+4

$15 x^{2} + 16 x + 4$

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 $a \cdot c = 15 \cdot 4 = 60$ and whose sum is $b = 16$ .

Factor $16$ out of $16 x$ .

$15 x^{2} + 16 (x) + 4$

Rewrite $16$ as $6$ plus $10$

$15 x^{2} + (6 + 10) x + 4$

Apply the distributive property.

$15 x^{2} + 6 x + 10 x + 4$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(15 x^{2} + 6 x) + 10 x + 4$

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

$3 x (5 x + 2) + 2 (5 x + 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x + 2$ .

$(5 x + 2) (3 x + 2)$

Factor 15x^2+16x+4

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