How do you express x3−5x+2x2−8x+15 in partial fractions?

1 Answer
George C.
Aug 7, 2016

x3−5x+2x2−8x+15=x+8−7x−3+51x−5

Explanation:

x3−5x+2x2−8x+15

=x3−8x2+15x+8x2−64x+120+44x−118x2−8x+15

=x(x2−8x+15)+8(x2−8x+15)+44x−118x2−8x+15

=x+8+44x−118x2−8x+15

=x+8+44x−118(x−3)(x−5)

=x+8+Ax−3+Bx−5

Using Heaviside's cover-up method, we find:

A=44(3)−118(3)−5=132−118−2=14−2=−7

B=44(5)−118(5)−3=220−1182=1022=51

So:

x3−5x+2x2−8x+15=x+8−7x−3+51x−5

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