Basic Math Examples

$2 p^{2} - 5 p q - 3 q^{2}$

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

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Step 1.1

Reorder terms.

$2 p^{2} - 3 q^{2} - 5 p q$

Step 1.2

Reorder $- 3 q^{2}$ and $- 5 p q$ .

$2 p^{2} - 5 p q - 3 q^{2}$

Step 1.3

Factor $- 5$ out of $- 5 p q$ .

$2 p^{2} - 5 (p q) - 3 q^{2}$

Step 1.4

Rewrite $- 5$ as $1$ plus $- 6$

$2 p^{2} + (1 - 6) (p q) - 3 q^{2}$

Step 1.5

Apply the distributive property.

$2 p^{2} + 1 (p q) - 6 (p q) - 3 q^{2}$

Step 1.6

Multiply $p q$ by $1$ .

$2 p^{2} + p q - 6 (p q) - 3 q^{2}$

Step 1.7

Remove unnecessary parentheses.

$2 p^{2} + p q - 6 p q - 3 q^{2}$

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.

$(2 p^{2} + p q) - 6 p q - 3 q^{2}$

Step 2.2

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

$p (2 p + q) - 3 q (2 p + q)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 p + q$ .

$(2 p + q) (p - 3 q)$