Pre-Algebra Examples

$(4 x^{2} + 25 x - 20) \div (x + 7)$

Step 1

Write $(4 x^{2} + 25 x - 20) \div (x + 7)$ as an equation.

$y = (4 x^{2} + 25 x - 20) \div (x + 7)$

Step 2

Simplify $(4 x^{2} + 25 x - 20) \div (x + 7)$ .

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Step 2.1

Rewrite the division as a fraction.

$y = \frac{4 x^{2} + 25 x - 20}{x + 7}$

Step 2.2

Split the fraction $\frac{4 x^{2} + 25 x - 20}{x + 7}$ into two fractions.

$y = \frac{4 x^{2} + 25 x}{x + 7} + \frac{- 20}{x + 7}$

Step 2.3

Simplify each term.

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Step 2.3.1

Factor $x$ out of $4 x^{2} + 25 x$ .

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Step 2.3.1.1

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

$y = \frac{x (4 x) + 25 x}{x + 7} + \frac{- 20}{x + 7}$

Step 2.3.1.2

Factor $x$ out of $25 x$ .

$y = \frac{x (4 x) + x \cdot 25}{x + 7} + \frac{- 20}{x + 7}$

Step 2.3.1.3

Factor $x$ out of $x (4 x) + x \cdot 25$ .

$y = \frac{x (4 x + 25)}{x + 7} + \frac{- 20}{x + 7}$

Step 2.3.2

Move the negative in front of the fraction.

$y = \frac{x (4 x + 25)}{x + 7} - \frac{20}{x + 7}$

Step 3

Combine the numerators over the common denominator.

$y = \frac{x (4 x + 25) - 20}{x + 7}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$y = \frac{x (4 x) + x \cdot 25 - 20}{x + 7}$

Step 4.2

Rewrite using the commutative property of multiplication.

$y = \frac{4 x \cdot x + x \cdot 25 - 20}{x + 7}$

Step 4.3

Move $25$ to the left of $x$ .

$y = \frac{4 x \cdot x + 25 \cdot x - 20}{x + 7}$

Step 4.4

Multiply $x$ by $x$ by adding the exponents.

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Step 4.4.1

Move $x$ .

$y = \frac{4 (x \cdot x) + 25 \cdot x - 20}{x + 7}$

Step 4.4.2

Multiply $x$ by $x$ .

$y = \frac{4 x^{2} + 25 \cdot x - 20}{x + 7}$

$y = \frac{4 x^{2} + 25 x - 20}{x + 7}$

Step 5

The given equation $y = \frac{4 x^{2} + 25 x - 20}{x + 7}$ can not be written as $y = k x^{2}$ , so $y$ doesn't vary directly with $x^{2}$ .

$y$ doesn't vary directly with $x$