Which expression is the factorization of x2 + 10x + 21?
A. (x + 3)(x + 7)
B. (x + 4)(x + 6)
C. (x + 6)(x + 15)
D. (x + 7)(x + 14)
I'm on a timed test so please hurry!
multiply the two numbers in each binomial pair ... you're looking for 21
Which expression is the factorization of x2 + 10x + 21?
To factorize the expression x^2 + 10x + 21, we need to find two binomials whose product gives us the original expression. Let's break it down step by step:
Step 1: We need to find two numbers that multiply to give us the last term, which is 21, and add up to give us the coefficient of the middle term, which is 10.
The numbers that fit these criteria are 3 and 7 since 3 * 7 = 21 and 3 + 7 = 10.
Step 2: Now we can write the expression as the product of two binomials using these numbers:
(x + 3)(x + 7)
So, the factorization of x^2 + 10x + 21 is:
A. (x + 3)(x + 7)
Please note that answer choices B, C, and D do not accurately represent the factorization of the given expression.
To factorize a quadratic expression like x^2 + 10x + 21, you need to find two binomials whose product equals the given expression.
One quick way to do this is by using the FOIL method. FOIL stands for First, Outer, Inner, Last, which is a way to expand the product of two binomials. Let's see how it works:
Start by breaking down the middle term, which is 10x, into two terms that multiply to give you 21. In this case, the two terms are 3x and 7x since 3x * 7x = 21x (the coefficients add up to 10x).
Now, we can rewrite the expression as follows:
x^2 + 3x + 7x + 21
Next, group the terms in pairs:
(x^2 + 3x) + (7x + 21)
Now, factor out the greatest common factor from each pair:
x(x + 3) + 7(x + 3)
Notice that we now have a common binomial factor of (x + 3). We can factor it out:
(x + 3)(x + 7)
Therefore, the factorization of x^2 + 10x + 21 is (x + 3)(x + 7).
Considering the answer choices given, the correct factorization is:
A. (x + 3)(x + 7)
I hope this explanation helps, and good luck on your timed test!