Pre-Algebra Examples

$\frac{4 x^{2} - 19 x - 5}{x - 5}$

Step 1

Factor by grouping.

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Step 1.1

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 $a \cdot c = 4 \cdot - 5 = - 20$ and whose sum is $b = - 19$ .

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Step 1.1.1

Factor $- 19$ out of $- 19 x$ .

$\frac{4 x^{2} - 19 (x) - 5}{x - 5}$

Step 1.1.2

Rewrite $- 19$ as $1$ plus $- 20$

$\frac{4 x^{2} + (1 - 20) x - 5}{x - 5}$

Step 1.1.3

Apply the distributive property.

$\frac{4 x^{2} + 1 x - 20 x - 5}{x - 5}$

Step 1.1.4

Multiply $x$ by $1$ .

$\frac{4 x^{2} + x - 20 x - 5}{x - 5}$

Step 1.2

Factor out the greatest common factor from each group.

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Step 1.2.1

Group the first two terms and the last two terms.

$\frac{(4 x^{2} + x) - 20 x - 5}{x - 5}$

Step 1.2.2

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

$\frac{x (4 x + 1) - 5 (4 x + 1)}{x - 5}$

Step 1.3

Factor the polynomial by factoring out the greatest common factor, $4 x + 1$ .

$\frac{(4 x + 1) (x - 5)}{x - 5}$

Step 2

Cancel the common factor of $x - 5$ .

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Step 2.1

Cancel the common factor.

$\frac{(4 x + 1) (x - 5)}{x - 5}$

Step 2.2

Divide $4 x + 1$ by $1$ .

$4 x + 1$