Basic Math Examples

$(6 a^{2} + 10 a + 4) \div (3 a + 1)$

Step 1

Rewrite the division as a fraction.

$\frac{6 a^{2} + 10 a + 4}{3 a + 1}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $2$ out of $6 a^{2} + 10 a + 4$ .

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Step 2.1.1

Factor $2$ out of $6 a^{2}$ .

$\frac{2 (3 a^{2}) + 10 a + 4}{3 a + 1}$

Step 2.1.2

Factor $2$ out of $10 a$ .

$\frac{2 (3 a^{2}) + 2 (5 a) + 4}{3 a + 1}$

Step 2.1.3

Factor $2$ out of $4$ .

$\frac{2 (3 a^{2}) + 2 (5 a) + 2 (2)}{3 a + 1}$

Step 2.1.4

Factor $2$ out of $2 (3 a^{2}) + 2 (5 a)$ .

$\frac{2 (3 a^{2} + 5 a) + 2 (2)}{3 a + 1}$

Step 2.1.5

Factor $2$ out of $2 (3 a^{2} + 5 a) + 2 (2)$ .

$\frac{2 (3 a^{2} + 5 a + 2)}{3 a + 1}$

Step 2.2

Factor by grouping.

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Step 2.2.1

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 $a \cdot c = 3 \cdot 2 = 6$ and whose sum is $b = 5$ .

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Step 2.2.1.1

Factor $5$ out of $5 a$ .

$\frac{2 (3 a^{2} + 5 (a) + 2)}{3 a + 1}$

Step 2.2.1.2

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

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

Step 2.2.1.3

Apply the distributive property.

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

Step 2.2.2

Factor out the greatest common factor from each group.

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Step 2.2.2.1

Group the first two terms and the last two terms.

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

Step 2.2.2.2

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

$\frac{2 (a (3 a + 2) + 1 (3 a + 2))}{3 a + 1}$

Step 2.2.3

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

$\frac{2 ((3 a + 2) (a + 1))}{3 a + 1}$

$\frac{2 (3 a + 2) (a + 1)}{3 a + 1}$