Algebra Examples

$3 x^{2} + 7 x - 20$

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 $a \cdot c = 3 \cdot - 20 = - 60$ and whose sum is $b = 7$ .

Tap for more steps...

Step 1.1

Factor $7$ out of $7 x$ .

$3 x^{2} + 7 (x) - 20$

Step 1.2

Rewrite $7$ as $- 5$ plus $12$

$3 x^{2} + (- 5 + 12) x - 20$

Step 1.3

Apply the distributive property.

$3 x^{2} - 5 x + 12 x - 20$

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.

$(3 x^{2} - 5 x) + 12 x - 20$

Step 2.2

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

$x (3 x - 5) + 4 (3 x - 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x - 5$ .

$(3 x - 5) (x + 4)$