Question

How do you factor the trinomial `3x^2 + 12x + 7`?

Answer 1

To factor the trinomial, we use the quadratic formula to solve for the zeros, which are `(-6+-sqrt(15))/(3)` or `-0.71` and `-3.29`.

Explanation:

Since there is no common factor between any of the three terms, we have to use the quadratic formula:

`a=3`
`b=12`
`c=7`

`x=(-b+-sqrt(b^2-4ac))/(2a)`

`x=(-(12)+-sqrt((12)^2-4(3)(7)))/(2(3))`

`x=(-12+-sqrt((144)-(84)))/6`

`x=(-12+-sqrt(60))/6`

`x=(-12+-2sqrt(15))/6`

`x=(2(-6+-1sqrt(15)))/(2(3))`

`x=(color(red)cancelcolor(black)(2)(-6+-1sqrt(15)))/(color(red)cancelcolor(black)(2)(3))`

`x=(-6+-sqrt(15))/(3)`

`x=-0.71` or `-3.29`

If your answer is supposed to be exact, your answer is:

`x=(-6+-sqrt(15))/(3)`

Otherwise, you can continue to solve for the approximate values of `x`.