How do you factor #5x^4-40x+10x^3-20x^2#?

1 Answer
Jim G.
Mar 27, 2018

#5x(x-2)(x+2)^2#

Explanation:

#"take out a "color(blue)"common factor "5x#

#5x(x^3-8+2x^2-4x)#

#"note that "2^3-8+2(2)^2-4(2)=0#

#rArr(x-2)" is a factor of "x^3+2x^2-4x-8#

#"divide "x^3+2x^2-4x-8" by "(x-2)#

#rArrcolor(red)(x^2)(x-2)color(magenta)(+2x^2)+2x^2-4x-8#

#=color(red)(x^2)(x-2)color(red)(+4x)(x-2)color(magenta)(+8x)-4x-8#

#=color(red)(x^2)(x-2)color(red)(+4x)(x-2)color(red)(+4)(x-2)cancel(color(magenta)(+8))cancel(-8)#

#rArrx^3+2x^2-4x-8=(x-2)(color(red)(x^2+4x+4))#

#color(white)(xxxxxxxxxxxxxxx)=(x-2)(x+2)^2#

#rArr5x^4-40x+10x^3-20x^2#

#=5x(x-2)(x+2)^2#

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