Factor by Grouping

3x² +8x + 4
Product of (a)(c) = (3)(4) = 12
What factors of 12 sum to 8?

Answer

2 & 6
Think of 8x as 2x + 6x
3x² + 2x + 6x + 4
Group the 2 pairs : (3x² + 2x) + (6x + 4)
Remove the common factors:: x(3x + 2) + 2(3x + 2)
Rewrite as grouped factors: (x + 2)(3x + 1)

3x² + 7x + 4
Product of (a)(c) = (3)(4) = 12
What factors of 12 sum to 7?

Answer

3 & 4
Think of 7x as 3x + 4x
3x² + 3x + 4x + 4
Group the 2 pairs : (3x² + 3x) + (4x + 4)
Remove the common factors: 3x(x + 1) + 4(x + 1)
Rewrite as grouped factors: (3x + 4)(x + 1)

5x² + 18x + 9

Show Factors By Grouping

Product of (a)(c) = (5)(9) = 45
What factors of 45 sum to 18?
3 & 15
Think of 18x as 3x + 15x
5x² + 3x + 15x + 9
Group the 2 pairs : (5x² + 3x) + (15x + 9)
Remove the common factors: x(5x + 3) + 3(5x + 3)
Rewrite as grouped factors: (x + 3)(5x + 3)