Explain how you would factor x^2-5x-24
You must explain EACH step and process t get to your factored solution
The work I have done
- (x-8)(x+3)
I just don't understand how to explain.
the numbers in the binary factors are factors of the constant term of the quadratic (-24)
the sum of the numbers is the coefficient of the 1st order term of the quadratic (-5)
the numbers -8 and 3 are factors of -24 that sum to -5
so the factors of the quadratic are
... (x - 8) and (x + 3)
yadda...yadda...yadda
To factor the quadratic expression x^2 - 5x - 24, you can use a method called factoring by grouping. Here are the steps to follow:
Step 1: Write down the quadratic expression: x^2 - 5x - 24.
Step 2: Split the middle term (-5x) into two terms that when combined will give you the original middle term, but when multiplied together will give you the product of the first and last terms (x^2 and -24).
To do this, we need to find two numbers that multiply to -24 and add up to -5. The numbers in this case are -8 and 3 since -8 * 3 = -24 and -8 + 3 = -5.
Step 3: Replace the middle term (-5x) with -8x + 3x, using the numbers found in step 2.
Now the expression becomes: x^2 - 8x + 3x - 24.
Step 4: Group the terms. Group the first two terms together and the last two terms together:
(x^2 - 8x) + (3x - 24).
Step 5: Factor out the greatest common factor from each group. Factor out an x from the first group and a 3 from the second group:
x(x - 8) + 3(x - 8).
Step 6: Notice that both groups have a common factor of (x - 8). Factor it out:
(x - 8)(x + 3).
And that's the factored form of the quadratic expression x^2 - 5x - 24.