How do you factor x3−7x2=−5x−35?

1 Answer
Andy Y.
Mar 14, 2016

(x+1.74)(x+4.37−1.04i)(x−4.37+1.04i)≈0

Explanation:

First, graph the left and right sides of the equation to determine approximately where they intersect:

graph{(y-x^3+7x^2)(y+5x+35)=0 [-5, 8, -55, 20]}

They intersect around x=−1.74, which creates our first factor x+1.74=0. A graphing calculator can give you even greater accuracy (e.g., my TI-83 says x≈−1.7358)

Next, use long division to determine the remaining quadratic. The result of long division (ignoring the very small remainder) gives,

x3−7x2+5x+35x+1.74≈x2−8.74x+20.16

Plugging this into the quadratic equation gives you the remaining imaginary factors:

x≈−4.37+1.04i or x≈4.37−1.04i

All three factors multiplied together gives

(x+1.74)(x+4.37−1.04i)(x−4.37+1.04i)≈0

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