What is the factored form of 8x2-8x-16?

Answer 1

Here you have the prime example of a trinomial. It consists of three terms (8x², -8x, and -16).

When factoring any nominal, we begin by looking for a common factor shared by all terms.

What is common between 8x², -8x, and -16? Let's break it down and see.

• 8x² = 2 • 2 • 2 • x • x
• -8x = 2 • 2 • 2 • x
• -16 = 2 • 2 • 2 • 2

Let's go ahead and bold all the numbers (constants) and variables that are similar in the groups.

• 8x² = 2 • 2 • 2 • x • x
• -8x = 2 • 2 • 2 • x
• -16 = 2 • 2 • 2 • 2

So it appears each term has a GCF (Greatest Common Factor) of 8 (2 • 2 = 4 • 2 = 8).

Now we simply pull the 8 out of each term.

8(x²-x-2)

Now we need to remember the rule that says: a • c = a + c = b. This says that when "a" is multiplied by "c", the addition of the two numbers by equal to the center number.

In our case here, a is x, b is -x, and c is -2.

a • c = x • -2 = -2

So now we need to find two numbers that when multiplied make -2, but when added make -1 (x's always equal to one).

• -2 = 2 • -1, when we add them 2 + (-1) = -1. These are our "magic numbers".

Now we simply plug in our numbers keeping the variable with each one.

8(x²-1x+2x-2)

Now we have a polynomial. These are very easy to factor. We simply break them up into two sets of two terms and remove the common factor's.

8(x² - 1x) + (2x - 2)

8(x(x + 1) + 2(x - 1))

Now we just rewrite our problem using the numbers on the inside and the numbers on the outside.

8(x+1)(x-2)

There you have it, the factored form of 8x²-8x-16 = 8(x+1)(x-2).