is x^2.x^2 + 7x + 12 = (x )(x )- Look at the number at the end of the expression you are trying to factor. Write down its factors.
In this case, the factors of 12 are 1 and 12, 2 and 6, and 3 and 4.
Factoring
When factoring an equa-
tion like x^2 + bx + c, think
“A.M.” Find two numbers
that Add up to the middle
term (b) and Multiply to
give the last term (c).- To determine which set of factors to put in the parentheses, look at the coefficient of the middle
term of the quadratic expression. In this case, the coefficient is 7. So, the correct factors will
also either add or subtract to get 7. Write the correct factors in the parentheses.
x^2 + 7x + 12 = (x __ 3)(x __ 4)- Finally, determine the signs for the factors. To get a positive 12, the 3 and the 4 are either both
positive or both negative. But, since 7 is also positive, the signs must both be positive.
x^2 + 7x + 12 = (x + 3)(x + 4)You can always check that you have factored correctly by FOILing the factors to see if you get the original
quadratic expression.
Now, try this one:
16.In the expression x^2 + kx + 12, k is a negative integer. Which of the following is a possiblevalue of k ?A) −13
B) −12
C) −6
D) 7Here’s How to Crack It
Since the question told you that k is a negative integer, you can immediately eliminate (D) because it is a
positive integer. To solve the question, you need to factor. This question is just a twist on the example
used above. Don’t worry that we don’t know the value of k. The question said that k was an integer, so
you need to consider only the integer factors of 12. The possible factors of 12 are 1 and 12, 2 and 6, and 3