How do you factor the polynomials 48tu−90t+32u−60?
1 Answer
Apr 28, 2017
Explanation:
Given:
48tu−90t+32u−60
Note that the ratio of the first and second terms is the same as the ratio of the third and fourth terms. So this quadrinomial will factor by grouping.
First separate out the common scalar factor
48tu−90t+32u−60=2(24tu−45t+16u−30)
48tu−90t+32u−60=2((24tu−45t)+(16u−30))
48tu−90t+32u−60=2(3t(8u−15)+2(8u−15))
48tu−90t+32u−60=2(3t+2)(8u−15)
As an alternative, we could swap the middle two terms before grouping, which may make the arithmetic seem a little easier:
48tu−90t+32u−60=48tu+32u−90t−60
48tu−90t+32u−60=2(24tu+16u−45t−30)
48tu−90t+32u−60=2((24tu+16u)−(45t+30))
48tu−90t+32u−60=2(8u(3t+2)−15(3t+2))
48tu−90t+32u−60=2(8u−15)(3t+2)
