Algebra Examples

$3 x^{2} + 8 x + 5$

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 $a \cdot c = 3 \cdot 5 = 15$ and whose sum is $b = 8$ .

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Step 1.1

Factor $8$ out of $8 x$ .

$3 x^{2} + 8 (x) + 5$

Step 1.2

Rewrite $8$ as $3$ plus $5$

$3 x^{2} + (3 + 5) x + 5$

Step 1.3

Apply the distributive property.

$3 x^{2} + 3 x + 5 x + 5$

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.

$(3 x^{2} + 3 x) + 5 x + 5$

Step 2.2

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

$3 x (x + 1) + 5 (x + 1)$

Step 3

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

$(x + 1) (3 x + 5)$