# How do you factor # 4x^3 - x^2 -12x + 3# by grouping?

##### 1 Answer

#### Explanation:

Think of this cubic as two groups:

#overbrace((4x^3-x^2))^"Group 1"+overbrace((-12x+3))^"Group 2"#

We will want to find a common factor in each group. From

#overbrace(x^2(4x-1))^"Group 1"+overbrace((-12x+3))^"Group 2"#

From Group 2, we could either factor out a

#overbrace(x^2(4x-1))^"Group 1"+overbrace(-3(4x-1))^"Group 2"#

From here, notice that there is a common factor between Group 1 and Group 2. Both have terms,

#(4x-1)(x^2-3)#

Depending on your level of instruction, you may recognize that