How do you factor 5x^4-40x+10x^3-20x^2?
1 Answer
Mar 27, 2018
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
