# How do you factor the polynomials #48tu-90t+32u-60#?

##### 1 Answer

#### 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)#

#color(white)(48tu-90t+32u-60) = 2((24tu-45t)+(16u-30))#

#color(white)(48tu-90t+32u-60) = 2(3t(8u-15)+2(8u-15))#

#color(white)(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#

#color(white)(48tu-90t+32u-60) = 2(24tu+16u-45t-30)#

#color(white)(48tu-90t+32u-60) = 2((24tu+16u)-(45t+30))#

#color(white)(48tu-90t+32u-60) = 2(8u(3t+2)-15(3t+2))#

#color(white)(48tu-90t+32u-60) = 2(8u-15)(3t+2)#