10x^2+15x-20
How do you factor this one? Please help...
I don't get it at all.
Actually, I got it.
Thanks for your help Steve.
Answer: 5(2x^2+3x-4)
To factor the quadratic expression 10x^2 + 15x - 20, we can use a method called "factoring by grouping." Here's how you do it step by step:
Step 1: Look at the coefficient of the x^2 term (10) and the constant term (-20). Determine if there is a common factor between them. In this case, the largest common factor is 5.
Step 2: Rewrite the quadratic expression by factoring out the common factor (5) from the first two terms:
10x^2 + 15x - 20
= 5(2x^2 + 3x - 4)
Step 3: Now, we need to focus on factoring the expression (2x^2 + 3x - 4). To do this, we will split the middle term (3x) into two terms in such a way that the product of the coefficient of x^2 term (2) and the constant term (-4) can be simplified.
We need to find two numbers that multiply to give -8 (2 * -4) and add up to 3.
Step 4: After experimenting, we find that 4 and -2 are the numbers that meet the criteria. We rewrite the expression:
2x^2 + 3x - 4
= 2x^2 + 4x - 2x - 4
Step 5: We group the terms:
(2x^2 + 4x) - (2x + 4)
Step 6: Now, we can factor out the common factors from each group:
2x(x + 2) - 2(x + 2)
Step 7: Notice that (x + 2) appears as a common term in both groups. We can factor this common term out:
(2x - 2)(x + 2)
So, the factored form of the quadratic expression 10x^2 + 15x - 20 is (2x - 2)(x + 2).
You can check your answer by expanding this factored form using the distributive property, and you should get back the original expression.