Respuesta :

chetankachana

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]

Otras preguntas