Answer:
x^2 - 16x + 48 = (x - 4)(x - 12)
Step-by-step explanation:
To factor a trinomial of the form
x^2 + ax + b,
find two numbers that multiply to b and add to a. Let's call them p and q.
Then the factorization is
x^2 + ax + b = (x + p)(x + q)
In this case, you have
x^2 - 16x + 48
a = -16, and b = 48.
You need two numbers that multiply to b, 48.
The two numbers must add to -16.
Since the numbers must multiply to a positive number, 48, they must be both positive or both negative. Since the numbers must add to -16, and they must be both positive or both negative from the product, then they must be both negative. Now we look for pairs of negative numbers that multiply to 48. We also write their sum. If they add to -16, they are the two numbers we need.
Try -1 and -48:
-1 * (-48) = 48; sum = -1 + (-48) = -49; not -16
Try -2 and -24:
-2 * (-24) = 48; sum = -2 + (-24) = -26; not -16
Try -3 and -16:
-3 * (-16) = 48; sum = -3 + (-16) = -19; not -16
Try -4 and -12:
-4 * (-12) = 48; sum = -4 + (-12) = -16; sum is -16; the sum we need
-4 and -12 work.
The two numbers, p and q, are -4 and -12.
x^2 - 16x + 48 = (x - 4)(x - 12)
