How do you factor y=x5−16x3+8x2−128 ?
1 Answer
Jan 6, 2016
Factor by grouping then using a couple of identities to find:
x5−16x3+8x2−128=(x+2)(x2−2x+4)(x−4)(x+4)
Explanation:
The sum of cubes identity can be written:
a3+b3=(a+b)(a2−ab+b2)
The difference of squares identity can be written:
a2−b2=(a−b)(a+b)
Factor by grouping then use these two identities as follows:
x5−16x3+8x2−128
=(x5−16x3)+(8x2−128)
=x3(x2−16)+8(x2−16)
=(x3+8)(x2−16)
=(x3+23)(x2−42)
=(x+2)(x2−(x)(2)+22)(x−4)(x+4)
=(x+2)(x2−2x+4)(x−4)(x+4)
