Question

Factor completely: 3x2 + 12x + 7

1. (3x + 1)(x + 7)

2. (3x + 7)(x + 1)

3. Prime

4. (3x + 4)(x + 3)

Answer 1

Answer: C

Given : Quadratic equation

To find : The factors of given equation.

Solution : To factories the given equation

We will apply discriminant method

General form -

Solution is

Equation is

where a=3 , b=1, c=7

Solution is

Therefore, The factors are

So, 1,2,4 are not the options.

Now, check for prime

In a quadratic equation if form a complete square then it is not prime and vice-versa.

In this question does not make a perfect square.

Therefore, It is a prime.

Option 3 is correct.

Explanation:

Answer 2

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.