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

Question

3209 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-09T20:11:57

Try x = -2.
#f(-2)= -8 + 8 +16 - 16 = 0. #Then f(x) can be divided by (x + 2)

#f(x) = (x + 2)(x^2 - 8).#

Answer 2 · 2015-05-09T20:26:03

The answer is #(x^2-8)(x+4)# .

Factor #x^3+2x^2-8x-16# .

Since there is no common factor for the polynomial, factor by grouping.

#color(red)(x^3+2x^2)color(blue)(-(8x-16)#

Factor #color(red)x^2# out of the first term.

#color(red)(x^2(x+2)#

Factor #color(blue)(-8# out of the second term.

#color(blue)(-8(x+2)#

Put the two sets of terms back together.

#color(red)(x^2(x+2)color(blue)(-8(x+2)#

#color(purple)((x+2)# is now the common factor.

Factor out #color(purple)((x+2)# .

Final answer = #color(purple)((x^2-8)(x+2)#