Question

Factor 18x^(2)+39x-15

Answer 1

`3(2x + 5)(3x - 1)`

Explanation:

Hello!

We can first factor out the greatest common factor between the coefficients: 3.

• 
  `f(x) = 18x^2 + 39x - 15`
• 
  `f(x) = 3(6x^2 + 13x - 5)`

Now, let's work with what we have inside the brackets.

Standard form of a quadratic:
`ax^2 + bx+ c = 0`

Given our equation:
`6x^2 + 13x - 5`

• a = 6
• b = 13
• c = -5

We need to find two numbers that add up to b (13) and multiply to ac (-30).

The two numbers are 15 and -2. Expand 13x to 15x and -2x and factor by grouping.

Factor by Grouping

• 
  `6x^2 + 13x - 5`
• 
  `6x^2 -2x + 15x - 5`
• 
  `2x(3x- 1) +5(3x - 1)`
• 
  `(2x +5)(3x - 1)`

Now, we simply add the other factor, 3, to the final factored form.

Factored Solution:
`3(2x + 5)(3x - 1)`