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

1 Answer
Nov 21, 2015

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.