Factor 5x^2 -6x-4
I must be having an off day or something; this can factor, right!?
Erm...no....it can't.
Okay, well, I don't know how the tracher's getting her answers then.,.
Yes, the expression 5x^2 - 6x - 4 can indeed be factored. To factor a quadratic expression like this, we need to find two binomials that, when multiplied together, give us the original expression.
Here's how we can do it step by step:
Step 1: Multiply the coefficient of x^2 (which is 5) by the constant term (which is -4). In this case, 5 * -4 = -20.
Step 2: Now, we need to look for two numbers that multiply to give us -20 and add up to the coefficient of the x-term (which is -6). In this case, the numbers we're looking for are -10 and 2 because -10 * 2 = -20 and -10 + 2 = -6.
Step 3: Rewrite the middle term (-6x) using the two numbers we found in the previous step. So instead of -6x, we write -10x + 2x, since -10 + 2 = -6.
Now, let's rewrite the expression:
5x^2 -10x + 2x - 4
Step 4: Group the terms and factor out the greatest common factor from each group.
(5x^2 -10x) + (2x - 4)
= 5x(x - 2) + 2(x - 2)
Step 5: Notice that we have a common binomial factor (x - 2) in both groups. We can factor it out.
= (x - 2)(5x + 2)
And that's it! The factored form of 5x^2 - 6x - 4 is (x - 2)(5x + 2).