What is ((-24x^3+18x+6))/((6x+3)) ?

The solution to ((-24x^3+18x+6))/((6x+3)) is -2(x-1)(2x+1)

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simplify ((-24x^3+18x+6))/((6x+3))

simplify

\frac{( - 24 x ^{3} + 18 x + 6 )}{( 6 x + 3 )}

- 2 (x - 1) (2 x + 1)

Solution steps

\frac{- 24 x ^{3} + 18 x + 6}{6 x + 3}

Factor

- 24 x^{3} + 18 x + 6 : - 6 (x - 1) (2 x + 1)^{2}

= \frac{- 6 ( x - 1 ) ( 2 x + 1 ) ^{2}}{6 x + 3}

Factor

6 x + 3 : 3 (2 x + 1)

= \frac{- 6 ( x - 1 ) ( 2 x + 1 ) ^{2}}{3 ( 2 x + 1 )}

Factor the number:

6 = 3 \cdot 2

= \frac{- 3 \cdot 2 ( x - 1 ) ( 2 x + 1 ) ^{2}}{3 ( 2 x + 1 )}

Cancel the common factor:

3

= \frac{- 2 ( x - 1 ) ( 2 x + 1 ) ^{2}}{2 x + 1}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(2 x + 1)^{2} = (2 x + 1) (2 x + 1)

= \frac{- 2 ( x - 1 ) ( 2 x + 1 ) ( 2 x + 1 )}{2 x + 1}

Cancel the common factor:

2 x + 1

= - 2 (x - 1) (2 x + 1)

a \cdot 2 a

6 \cdot 30

6 \cdot 11

- 77

2 \cdot 3 \cdot 5

What is ((-24x^3+18x+6))/((6x+3)) ?
The solution to ((-24x^3+18x+6))/((6x+3)) is -2(x-1)(2x+1)