What is (-4a^3-20a^2+16a+80)/(a-2) ?

The solution to (-4a^3-20a^2+16a+80)/(a-2) is -4(a+5)(a+2)

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simplify (-4a^3-20a^2+16a+80)/(a-2)

simplify

\frac{- 4 a ^{3} - 20 a ^{2} + 16 a + 80}{a - 2}

- 4 (a + 5) (a + 2)

Solution steps

\frac{- 4 a ^{3} - 20 a ^{2} + 16 a + 80}{a - 2}

Factor

- 4 a^{3} - 20 a^{2} + 16 a + 80 : 4 (- a^{3} - 5 a^{2} + 4 a + 20)

= \frac{4 ( - a ^{3} - 5 a ^{2} + 4 a + 20 )}{a - 2}

Factor out

- 1 : - (a^{3} + 5 a^{2} - 4 a - 20)

= \frac{- 4 ( a ^{3} + 5 a ^{2} - 4 a - 20 )}{a - 2}

= \frac{- 4 ( ( a ^{3} + 5 a ^{2} ) + ( - 4 a - 20 ) )}{a - 2}

Factor out

a^{2}

from

a^{3} + 5 a^{2} : a^{2} (a + 5)

Factor out

- 4

from

- 4 a - 20 : - 4 (a + 5)

= \frac{- 4 ( a ^{2} ( a + 5 ) - 4 ( a + 5 ) )}{a - 2}

Factor out common term

a + 5

= \frac{- 4 ( a + 5 ) ( a ^{2} - 4 )}{a - 2}

Factor

a^{2} - 4 : (a + 2) (a - 2)

= \frac{- 4 ( a + 5 ) ( a + 2 ) ( a - 2 )}{a - 2}

Cancel the common factor:

a - 2

= - 4 (a + 5) (a + 2)

3 w^{2} - 12 w = 0

y (3 x + 1) - 3 x - 1

- 13 < x + 9

x^{2} + 18 x + 78 = 0

(\frac{- 8}{2})^{2}

What is (-4a^3-20a^2+16a+80)/(a-2) ?
The solution to (-4a^3-20a^2+16a+80)/(a-2) is -4(a+5)(a+2)