Question

How do you factor x^4 + 2x^3 - 8x -16?

Answer 1

Answer :

$(x + 2) \times (x - 2) \times (x {}^{2} + 2x + 4)$

Step by step explanation :

$x {}^{4} + 2x {}^{3} - 8x - 16$

Factor out x^3 from the expression

$= > x {}^{3} \times (x + 2) - 8x - 16$

Factor out - 8 from the expression.

$= > x {}^{3} \times (x + 2) - 8(x + 2)$

Factor out x + 2 from the expression

$= > (x + 2) \times (x {}^{3} - 8)$

Write the number 8 in exponential form with an exponent of 3

$= > (x + 2 )\times (x {}^{3} - 2 {}^{3} )$

Using

$a {}^{3} - b {}^{3} = (a - b)(a {}^{2} + ab + b {}^{2} )$

, factor the expression

$= > (x + 2) \times (x - 2) \times (x {}^{2} + x \times 2 + 2 {}^{2} )$

Use the commutative property to reorder the terms

$= > (x - 2) \times (x {}^{2} + 2x + 2 {}^{2} )$

Evaluate the power

$= > (x - 2) \times (x {}^{2} + 2x + 4)$