Factor 6p^2+5p+1

$6 p^{2} + 5 p + 1$

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 $a \cdot c = 6 \cdot 1 = 6$ and whose sum is $b = 5$ .

Factor $5$ out of $5 p$ .

$6 p^{2} + 5 (p) + 1$

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

$6 p^{2} + (2 + 3) p + 1$

Apply the distributive property.

$6 p^{2} + 2 p + 3 p + 1$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(6 p^{2} + 2 p) + 3 p + 1$

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

$2 p (3 p + 1) + 1 (3 p + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 p + 1$ .

$(3 p + 1) (2 p + 1)$

Factor 6p^2+5p+1

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