What is factor (a+2)^2-8+a^3-2a ?

The solution to factor (a+2)^2-8+a^3-2a is (a-1)(a^2+2a+4)

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factor (a+2)^2-8+a^3-2a

factor

(a + 2)^{2} - 8 + a^{3} - 2 a

(a - 1) (a^{2} + 2 a + 4)

Solution steps

(a + 2)^{2} - 8 + a^{3} - 2 a

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

= a^{2} + 4 a + 4 - 8 + a^{3} - 2 a

Simplify

a^{2} + 4 a + 4 - 8 + a^{3} - 2 a : a^{3} + a^{2} + 2 a - 4

= a^{3} + a^{2} + 2 a - 4

Use the rational root theorem

a_{0} = 4, a_{n} = 1

The dividers of

a_{0} : 1, 2, 4,

The dividers of

a_{n} : 1

Therefore, check the following rational numbers:

\pm \frac{1 , 2 , 4}{1}

\frac{1}{1}

is a root of the expression, so factor out

a - 1

= (a - 1) \frac{a ^{3} + a ^{2} + 2 a - 4}{a - 1}

\frac{a ^{3} + a ^{2} + 2 a - 4}{a - 1} = a^{2} + 2 a + 4

= (a - 1) (a^{2} + 2 a + 4)

x^{8} - 9

16 x^{2 n} - 1

2 x (a - c) + 3 y (c - a) - 4 a z + 4 cz

e^{x} + e^{- x}

\frac{d}{d x} ((x) (y))

What is factor (a+2)^2-8+a^3-2a ?
The solution to factor (a+2)^2-8+a^3-2a is (a-1)(a^2+2a+4)