factor the expression 2x^8 + 4x^7 - 6x^6 + 4x^5

Question

If the GCF is 2x^5, what if the expression factored in simplified terms?

Answer 1

2x⁸+4x⁷-6x⁶+4x⁵=2x⁵(x³+2x²-3x+2).

Note that if the original expression had been -2x⁸+4x⁷-6x⁶+4x⁵, the cubic in parentheses would have factorised further:

2x⁵(-x³+2x²-3x+2)=-2x⁵(x-1)(x²-x+2). The cubic doesn't otherwise factor rationally.

Note that if the original expression had been 2x⁸+4x⁷+6x⁶+4x⁵, the cubic in parentheses would have factorised further:

2x⁵(x³+2x²+3x+2)=2x⁵(x+1)(x²+x+2). The cubic doesn't otherwise factor rationally.