Algebra Examples

3 x^{2} + 7 x + 2

$3 x^{2} + 7 x + 2$

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

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

$b = 7$ .

Tap for more steps...

Step 1.1

Factor

$7$ out of

$7 x$ .

$3 x^{2} + 7 (x) + 2$

Step 1.2

Rewrite

$7$ as

$1$ plus

$6$

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Multiply

$x$ by

$1$ .

$3 x^{2} + x + 6 x + 2$

Step 2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 2.1

Group the first two terms and the last two terms.

$(3 x^{2} + x) + 6 x + 2$

Step 2.2

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

$x (3 x + 1) + 2 (3 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor,

$3 x + 1$ .

$(3 x + 1) (x + 2)$