Algebra Examples

$5 x^{2} + 18 x - 8$

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 $a \cdot c = 5 \cdot - 8 = - 40$ and whose sum is $b = 18$ .

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Step 1.1

Factor $18$ out of $18 x$ .

$5 x^{2} + 18 (x) - 8$

Step 1.2

Rewrite $18$ as $- 2$ plus $20$

$5 x^{2} + (- 2 + 20) x - 8$

Step 1.3

Apply the distributive property.

$5 x^{2} - 2 x + 20 x - 8$

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.

$(5 x^{2} - 2 x) + 20 x - 8$

Step 2.2

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

$x (5 x - 2) + 4 (5 x - 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x - 2$ .

$(5 x - 2) (x + 4)$