Algebra Examples

Factor $3 h^{2} + 11 h + 6$

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 $a \cdot c = 3 \cdot 6 = 18$ and whose sum is $b = 11$ .

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Step 1.1

Factor $11$ out of $11 h$ .

$3 h^{2} + 11 (h) + 6$

Step 1.2

Rewrite $11$ as $2$ plus $9$

$3 h^{2} + (2 + 9) h + 6$

Step 1.3

Apply the distributive property.

$3 h^{2} + 2 h + 9 h + 6$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$(3 h^{2} + 2 h) + 9 h + 6$

Step 2.2

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

$h (3 h + 2) + 3 (3 h + 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 h + 2$ .

$(3 h + 2) (h + 3)$