Answer :
Answer:
[tex]3(2x + 5)(3x - 1)[/tex]
Step-by-step explanation:
Hello!
We can first factor out the greatest common factor between the coefficients: 3.
- [tex]f(x) = 18x^2 + 39x - 15[/tex]
- [tex]f(x) = 3(6x^2 + 13x - 5)[/tex]
Now, let's work with what we have inside the brackets.
Standard form of a quadratic: [tex]ax^2 + bx+ c = 0[/tex]
Given our equation: [tex]6x^2 + 13x - 5[/tex]
- 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
- [tex]6x^2 + 13x - 5[/tex]
- [tex]6x^2 -2x + 15x - 5[/tex]
- [tex]2x(3x- 1) +5(3x - 1)[/tex]
- [tex](2x +5)(3x - 1)[/tex]
Now, we simply add the other factor, 3, to the final factored form.
Factored Solution: [tex]3(2x + 5)(3x - 1)[/tex]