Algebra Examples

$(3 t^{4} + 4 t^{3} - 32 t^{2} - 5 t - 20) {(t + 4)}^{- 1}$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(3 t^{4} + 4 t^{3} - 32 t^{2} - 5 t - 20) \frac{1}{t + 4}$

Step 3

Multiply $3 t^{4} + 4 t^{3} - 32 t^{2} - 5 t - 20$ by $\frac{1}{t + 4}$ .

$\frac{3 t^{4} + 4 t^{3} - 32 t^{2} - 5 t - 20}{t + 4}$

Step 4

Split the fraction $\frac{3 t^{4} + 4 t^{3} - 32 t^{2} - 5 t - 20}{t + 4}$ into two fractions.

$\frac{3 t^{4} + 4 t^{3} - 32 t^{2} - 5 t}{t + 4} + \frac{- 20}{t + 4}$

Step 5

Simplify each term.

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Step 5.1

Factor $t$ out of $3 t^{4} + 4 t^{3} - 32 t^{2} - 5 t$ .

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Step 5.1.1

Factor $t$ out of $3 t^{4}$ .

$\frac{t (3 t^{3}) + 4 t^{3} - 32 t^{2} - 5 t}{t + 4} + \frac{- 20}{t + 4}$

Step 5.1.2

Factor $t$ out of $4 t^{3}$ .

$\frac{t (3 t^{3}) + t (4 t^{2}) - 32 t^{2} - 5 t}{t + 4} + \frac{- 20}{t + 4}$

Step 5.1.3

Factor $t$ out of $- 32 t^{2}$ .

$\frac{t (3 t^{3}) + t (4 t^{2}) + t (- 32 t) - 5 t}{t + 4} + \frac{- 20}{t + 4}$

Step 5.1.4

Factor $t$ out of $- 5 t$ .

$\frac{t (3 t^{3}) + t (4 t^{2}) + t (- 32 t) + t \cdot - 5}{t + 4} + \frac{- 20}{t + 4}$

Step 5.1.5

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

$\frac{t (3 t^{3} + 4 t^{2}) + t (- 32 t) + t \cdot - 5}{t + 4} + \frac{- 20}{t + 4}$

Step 5.1.6

Factor $t$ out of $t (3 t^{3} + 4 t^{2}) + t (- 32 t)$ .

$\frac{t (3 t^{3} + 4 t^{2} - 32 t) + t \cdot - 5}{t + 4} + \frac{- 20}{t + 4}$

Step 5.1.7

Factor $t$ out of $t (3 t^{3} + 4 t^{2} - 32 t) + t \cdot - 5$ .

$\frac{t (3 t^{3} + 4 t^{2} - 32 t - 5)}{t + 4} + \frac{- 20}{t + 4}$

Step 5.2

Move the negative in front of the fraction.

$\frac{t (3 t^{3} + 4 t^{2} - 32 t - 5)}{t + 4} - \frac{20}{t + 4}$