How do you factor the expression #3x - 9x^2#?

1 Answer
Feb 28, 2016

Answer:

#3x(1-3x)#

Explanation:

Recall that the greatest common factor is the largest number which two numbers can be divided by without producing a decimal . For example, the greatest common factor of #12# and #16# is #4#.

In addition, recall the distributive property: #a(b+c)=ab+ac#.

Factoring the Expression
#1#. Determine the greatest common factor for #color(red)3# and #color(blue)9#, which is #color(purple)3#. Using the distributive property, factor #color(purple)3# from the expression.

#color(red)3x-color(blue)9x^2#

#=color(purple)3(x-3x^2)#

#2#. Both terms, #color(orange)x# and #-3color(turquoise)(x^2)#, contain another common factor, #color(green)x#. Thus, factor out #color(green)x# from the expression.

#=3color(green)x(1-3x)#