Algebra Examples

$3 x^{2} - 14 x + 15$

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 $a \cdot c = 3 \cdot 15 = 45$ and whose sum is $b = - 14$ .

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Step 1.1

Factor $- 14$ out of $- 14 x$ .

$3 x^{2} - 14 (x) + 15$

Step 1.2

Rewrite $- 14$ as $- 5$ plus $- 9$

$3 x^{2} + (- 5 - 9) x + 15$

Step 1.3

Apply the distributive property.

$3 x^{2} - 5 x - 9 x + 15$

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.

$(3 x^{2} - 5 x) - 9 x + 15$

Step 2.2

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

$x (3 x - 5) - 3 (3 x - 5)$

Step 3

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

$(3 x - 5) (x - 3)$