How do you factor completely 2x^3 + 4x^2 + 6x + 12?
2 Answers
Dec 31, 2017
Explanation:
Moving
Take out
we can continue factoring
Using:
Dec 31, 2017
Explanation:
"take out "color(blue)"common factor of 2"
rArr2(x^3+2x^2+3x+6)
"when "x=-2tox^3+2x^2+3x+6=0
rArr(x+2)" is a factor"
color(red)(x^2)(x+2)cancel(color(magenta)(-2x^2))cancel(+2x^2)+3x+6
=color(red)(x^2)(x+2)color(red)(+3)(x+2)cancel(color(magenta)(-6))cancel(+6)
rArrx^3+2x^2+3x+6=(x+2)(x^2+3)
"factor "x^2+3
x^2+3=0rArrx^2=-3rArrx=+-sqrt3i
rArr2x^3+4x^2+6x+12
=2(x+2)(x+sqrt3i)(x-sqrt3i)