how do you factor -x^2-7x+10? thanks much
First, factor out a negative.
-(x^2 + 7x - 10)
-(x + 2)(x + 5)
Actually, it's not factorable. The only factors of 10 are 5 and 2. The 5 and 2 have to add up to be 7, so they both must be positive. However, the product of 5 and 2 must be -10, which cannot happen.
Is it possible to factor -4x^2-8x+16?
you can't factor it from there though, can you?
To factor the quadratic expression -x^2 - 7x + 10, follow these steps:
Step 1: Check if there is a common factor.
In this case, since all terms have negative signs, you can factor out -1 to make it easier, like this:
-1(x^2 + 7x - 10)
Step 2: Find two numbers that multiply to give the constant term (-10) and add up to give the coefficient of the middle term (7).
The numbers that satisfy these conditions are 10 and -1, because (-1) x (10) = -10 and (-1) + (10) = 9.
Step 3: Rewrite the middle term using the two numbers you found in the previous step.
-1(x^2 + 10x - x - 10)
Step 4: Group the terms in pairs and factor each group separately by finding their greatest common factors.
-1[(x^2 + 10x) + (-x - 10)]
-1[x(x + 10) - 1(x + 10)]
Step 5: Factor out the common binomial factor.
-1[(x - 1)(x + 10)]
Hence, -x^2 - 7x + 10 can be factored as -1(x - 1)(x + 10).