Pre-Algebra Examples

$f (x) = (4 z^{4} + 5 z^{2} - 1) \div (z - \frac{1}{4})$

Step 1

Rewrite the function as an equation.

$y = (4 z^{4} + 5 z^{2} - 1) \div (z - \frac{1}{4})$

Step 2

Simplify $(4 z^{4} + 5 z^{2} - 1) \div (z - \frac{1}{4})$ .

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Step 2.1

Rewrite the division as a fraction.

$y = \frac{4 z^{4} + 5 z^{2} - 1}{z - \frac{1}{4}}$

Step 2.2

Multiply the numerator and denominator of the fraction by $4$ .

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Step 2.2.1

Multiply $\frac{4 z^{4} + 5 z^{2} - 1}{z - \frac{1}{4}}$ by $\frac{4}{4}$ .

$y = \frac{4}{4} \cdot \frac{4 z^{4} + 5 z^{2} - 1}{z - \frac{1}{4}}$

Step 2.2.2

Combine.

$y = \frac{4 (4 z^{4} + 5 z^{2} - 1)}{4 (z - \frac{1}{4})}$

Step 2.3

Apply the distributive property.

$y = \frac{4 (4 z^{4}) + 4 (5 z^{2}) + 4 \cdot - 1}{4 z + 4 (- \frac{1}{4})}$

Step 2.4

Simplify terms.

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Step 2.4.1

Cancel the common factor of $4$ .

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Step 2.4.1.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$y = \frac{4 (4 z^{4}) + 4 (5 z^{2}) + 4 \cdot - 1}{4 z + 4 (\frac{- 1}{4})}$

Step 2.4.1.2

Cancel the common factor.

$y = \frac{4 (4 z^{4}) + 4 (5 z^{2}) + 4 \cdot - 1}{4 z + 4 (\frac{- 1}{4})}$

Step 2.4.1.3

Rewrite the expression.

$y = \frac{4 (4 z^{4}) + 4 (5 z^{2}) + 4 \cdot - 1}{4 z - 1}$

Step 2.4.2

Factor $4$ out of $4 \cdot 4 z^{4} + 4 \cdot 5 z^{2} + 4 \cdot - 1$ .

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Step 2.4.2.1

Factor $4$ out of $4 \cdot 4 z^{4}$ .

$y = \frac{4 (4 z^{4}) + 4 \cdot 5 z^{2} + 4 \cdot - 1}{4 z - 1}$

Step 2.4.2.2

Factor $4$ out of $4 \cdot 5 z^{2}$ .

$y = \frac{4 (4 z^{4}) + 4 (5 z^{2}) + 4 \cdot - 1}{4 z - 1}$

Step 2.4.2.3

Factor $4$ out of $4 \cdot - 1$ .

$y = \frac{4 (4 z^{4}) + 4 (5 z^{2}) + 4 (- 1)}{4 z - 1}$

Step 2.4.2.4

Factor $4$ out of $4 (4 z^{4}) + 4 (5 z^{2})$ .

$y = \frac{4 (4 z^{4} + 5 z^{2}) + 4 (- 1)}{4 z - 1}$

Step 2.4.2.5

Factor $4$ out of $4 (4 z^{4} + 5 z^{2}) + 4 (- 1)$ .

$y = \frac{4 (4 z^{4} + 5 z^{2} - 1)}{4 z - 1}$