Algebra Examples

5 x^{2} - 2 x - 7

$5 x^{2} - 2 x - 7$

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

$a \cdot c = 5 \cdot - 7 = - 35$ and whose sum is

$b = - 2$ .

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Step 1.1

Factor

$- 2$ out of

$- 2 x$ .

$5 x^{2} - 2 (x) - 7$

Step 1.2

Rewrite

$- 2$ as

$5$ plus

$- 7$

$5 x^{2} + (5 - 7) x - 7$

Step 1.3

Apply the distributive property.

$5 x^{2} + 5 x - 7 x - 7$

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.

$(5 x^{2} + 5 x) - 7 x - 7$

Step 2.2

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

$5 x (x + 1) - 7 (x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor,

$x + 1$ .

$(x + 1) (5 x - 7)$

$5 x^{2} - 2 x - 7$

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