Question

How do you factor these?

Answer 1

Hi there!

24. 6x² + 19x + 3
      1                 3    multiply 6 × 3 = 18
      6                 1    multiply 1 × 1 = 1
                               18 + 1 = 19
(x + 3)(6x + 1)

I just simply found the two factors of 6 and 3 that can add up to 19.
This way is useful when the a and c don't have much factors.


27. 5y² + 13y + 6
      1                 2    5 × 2 = 10
      5                 3    1 × 3 = 3
                               10 + 3 = 13
(x + 2)(5x + 3)


30. 16x² + 16x + 3
For this one, 16 has a lot of factors. So you can try "Grouping" method.
You multiply 16 and 3. 16 × 3 =48
Find the factors of 48 that can add up to 16.
Hmm.. 12 and 4 would be great.
Then rewrite the equation.

16x² + 12x + 4x + 3
We would factor 16x² + 12x and 4x + 3 separately. 
16x² + 12x                    4x + 3 can't be factored more.
4x(4x + 3)                     1(4x + 3)
(4x + 1)(4x + 3)


So your answers are....
24. (x + 3)(6x + 1)

27. (x + 2)(5x + 3)

30. (4x + 1)(4x + 3)
 

Hope this helped!!