Algebra Examples

$2 a^{2} + 1 + 3 a$

Step 1

Reorder terms.

$2 a^{2} + 3 a + 1$

Step 2

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 $a \cdot c = 2 \cdot 1 = 2$ and whose sum is $b = 3$ .

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Step 2.1

Factor $3$ out of $3 a$ .

$2 a^{2} + 3 (a) + 1$

Step 2.2

Rewrite $3$ as $1$ plus $2$

$2 a^{2} + (1 + 2) a + 1$

Step 2.3

Apply the distributive property.

$2 a^{2} + 1 a + 2 a + 1$

Step 2.4

Multiply $a$ by $1$ .

$2 a^{2} + a + 2 a + 1$

Step 3

Factor out the greatest common factor from each group.

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Step 3.1

Group the first two terms and the last two terms.

$(2 a^{2} + a) + 2 a + 1$

Step 3.2

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

$a (2 a + 1) + 1 (2 a + 1)$

Step 4

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

$(2 a + 1) (a + 1)$