Pre-Algebra Examples

$(4 x^{2} + 12 x - 40) \div (4 x + 20)$

Step 1

Rewrite the division as a fraction.

$\frac{4 x^{2} + 12 x - 40}{4 x + 20}$

Step 2

Cancel the common factor of $4 x^{2} + 12 x - 40$ and $4 x + 20$ .

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Step 2.1

Factor $4$ out of $4 x^{2}$ .

$\frac{4 (x^{2}) + 12 x - 40}{4 x + 20}$

Step 2.2

Factor $4$ out of $12 x$ .

$\frac{4 (x^{2}) + 4 (3 x) - 40}{4 x + 20}$

Step 2.3

Factor $4$ out of $4 (x^{2}) + 4 (3 x)$ .

$\frac{4 (x^{2} + 3 x) - 40}{4 x + 20}$

Step 2.4

Factor $4$ out of $- 40$ .

$\frac{4 (x^{2} + 3 x) + 4 \cdot - 10}{4 x + 20}$

Step 2.5

Factor $4$ out of $4 (x^{2} + 3 x) + 4 (- 10)$ .

$\frac{4 (x^{2} + 3 x - 10)}{4 x + 20}$

Step 2.6

Cancel the common factors.

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Step 2.6.1

Factor $4$ out of $4 x$ .

$\frac{4 (x^{2} + 3 x - 10)}{4 (x) + 20}$

Step 2.6.2

Factor $4$ out of $20$ .

$\frac{4 (x^{2} + 3 x - 10)}{4 x + 4 \cdot 5}$

Step 2.6.3

Factor $4$ out of $4 x + 4 \cdot 5$ .

$\frac{4 (x^{2} + 3 x - 10)}{4 (x + 5)}$

Step 2.6.4

Cancel the common factor.

$\frac{4 (x^{2} + 3 x - 10)}{4 (x + 5)}$

Step 2.6.5

Rewrite the expression.

$\frac{x^{2} + 3 x - 10}{x + 5}$

Step 3

Factor $x^{2} + 3 x - 10$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 10$ and whose sum is $3$ .

$- 2, 5$

Step 3.2

Write the factored form using these integers.

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

Step 4

Cancel the common factor of $x + 5$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Divide $x - 2$ by $1$ .

$x - 2$