How do you factor out x^3+5x-24?
I meant:
How do you factor out x^2+5x-24?
you see which of the factors of c (-24) add together to get 5. -24 factors into 8 and -3. the answer is (x-3)(x+8)
To factor the expression x^3 + 5x - 24, we can use a method called factoring by grouping. Here’s how you can do it:
Step 1: Look for two numbers whose sum is 5 and their product is -24.
In this case, the numbers are 8 and -3, since 8 + (-3) = 5 and 8 * (-3) = -24.
Step 2: Rewrite the middle term (5x) using the two numbers found in the previous step.
So, x^3 + 8x - 3x - 24.
Step 3: Group the terms and factor out a common factor from each group.
(x^3 + 8x) - (3x + 24)
Factoring out an x from the first group and a -3 from the second group, we get:
x(x^2 + 8) - 3(x + 8)
Step 4: Notice that we have a common binomial factor of (x + 8).
(x - 3)(x + 8)
Therefore, the factored form of x^3 + 5x - 24 is (x - 3)(x + 8).
By following these steps, we have successfully factored the given expression.