Question

Factor completely: 3x2 + 12x + 7

Answer 1

Answer:

Step-by-step explanation:

Eliminate answer 4 immediately, because (4)(3) is not 7.

Look at answer 2:  7x + 3x = 10x, which does not match the middle term 12x in the original polynomial.  Eliminate answer 2.

Look at answer 1:  1x + 21x = 22x, which does not match the middle term of the original polynomial.   Eliminate answer 1.

All quadratics have solutions.  Let's apply the quadratic formula to 3x^2 + 12x + 7:  Here a = 3, b = 12 and c = 7, so that the discriminant b²-4ac is

12²-4(3)(7), or 144 - 84, or 60.  Being positive, this tells us that the given poly has two real, unequal roots:

      -12 ± √60        -12 + 2√15                     -12 - 2√15

x = ----------------- = -------------------  and   x = --------------------

            3                         3                                     3

Normally, if c is a root, then x - c is a factor.

If we try this here, however, the resulting factors do not at all match any of your answer choices.

Don't be offended...but please ensure you have copied this problem down correctly.