I have the polynomial x^2+2x-8 and when I tried to factor it, I just ended up confusing myself. Can anyone please help make sense of this?
Can you think of two numbers which when multiplied give you -8 (the last number) and when added will give you +2 (the coefficient of the middle term) ?
How about 4 and -2, so .... (4)(-2 = -8 , 4 + (-2) = +2
x^2 + 2x - 8
= (x+4)(x-2)
If the coefficient of the square term is 1, like in x^2, follow the above method.
If there are factors, it will work.
Of course, I can help you with that! Factoring a quadratic polynomial like x^2+2x-8 can sometimes be challenging, but there are different methods you can use to simplify the process.
One common method is called "factoring by grouping." Here's how you can factor the given polynomial using this method:
Step 1: Multiply the coefficient of the x^2 term (which is 1) with the constant term (-8). In this case, 1*(-8) gives you -8.
Step 2: Find two numbers whose sum is equal to the coefficient of the x term (which is 2) and whose product is equal to the result from step 1. In this case, the numbers are 4 and -2 since 4 + (-2) = 2 and 4*(-2) = -8.
Step 3: Rewrite the quadratic expression by splitting the x term using the two numbers found in step 2. Replace the original x term (2x) with the sum of the two numbers (4x - 2x). Your new expression will be:
x^2 + 4x - 2x - 8
Step 4: Group the terms in pairs and factor out the common factors from each pair separately. In this case, we can group the first two terms (x^2 + 4x) and the next two terms (-2x - 8). Factoring out the common factors, we get:
x(x + 4) - 2(x + 4)
Step 5: Notice that you now have a common factor of (x + 4). Factor out this common binomial from the expression:
(x + 4)(x - 2)
And there you have it! The factored form of the polynomial x^2+2x-8 is (x + 4)(x - 2).