What are the factors for #2b^4 + 14b^3 - 16b -112#?

1 Answer
Jim G.
Mar 26, 2018

#2(b+7)(b-2)(b^2+2b+4)#

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)#

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