What are the factors for #2b^4 + 14b^3 - 16b -112#?
1 Answer
Mar 26, 2018
Explanation:
#"take out a "color(blue)"common factor of 2"#
#2(b^4+7b^3-8b-56)#
#"factor "b^4+7b^3-8b-56color(blue)" by grouping"#
#rArrcolor(red)(b^3)(b+7)color(red)(-8)(b+7)#
#"take out a common factor "(b+7)#
#=(b+7)(color(red)(b^3-8))#
#b^3-8" is a "color(blue)"difference of cubes"#
#•color(white)(x)a^3-b^3=(a-b)(a^2+ab+b^2)#
#"here "a=b" and "b=2#
#rArrb^3-8=(b-2)(b^2+2b+4)#
#rArr2b^4+14b^3-16b-112#
#=2(b+7)(b-2)(b^2+2b+4)#
