Algebra Examples

$(3 c^{4} + 6 c^{3} - 2 c + 4) {(c + 2)}^{- 1}$

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 $b^{- n} = \frac{1}{b^{n}}$ .

$(3 c^{4} + 6 c^{3} - 2 c + 4) \frac{1}{c + 2}$

Step 3

Multiply $3 c^{4} + 6 c^{3} - 2 c + 4$ by $\frac{1}{c + 2}$ .

$\frac{3 c^{4} + 6 c^{3} - 2 c + 4}{c + 2}$

Step 4

Split the fraction $\frac{3 c^{4} + 6 c^{3} - 2 c + 4}{c + 2}$ into two fractions.

$\frac{3 c^{4} + 6 c^{3} - 2 c}{c + 2} + \frac{4}{c + 2}$

Step 5

Factor $c$ out of $3 c^{4} + 6 c^{3} - 2 c$ .

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Step 5.1

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

$\frac{c (3 c^{3}) + 6 c^{3} - 2 c}{c + 2} + \frac{4}{c + 2}$

Step 5.2

Factor $c$ out of $6 c^{3}$ .

$\frac{c (3 c^{3}) + c (6 c^{2}) - 2 c}{c + 2} + \frac{4}{c + 2}$

Step 5.3

Factor $c$ out of $- 2 c$ .

$\frac{c (3 c^{3}) + c (6 c^{2}) + c \cdot - 2}{c + 2} + \frac{4}{c + 2}$

Step 5.4

Factor $c$ out of $c (3 c^{3}) + c (6 c^{2})$ .

$\frac{c (3 c^{3} + 6 c^{2}) + c \cdot - 2}{c + 2} + \frac{4}{c + 2}$

Step 5.5

Factor $c$ out of $c (3 c^{3} + 6 c^{2}) + c \cdot - 2$ .

$\frac{c (3 c^{3} + 6 c^{2} - 2)}{c + 2} + \frac{4}{c + 2}$