I used the U-substitution
x + 1 = u
u^2 -11u + 24
(u + 3)(u - 8)
( x + 1 + 3) ( x + 1 - 8)
(x + 4) ( X - 7 )
Is this correct?
correct.
There is an apparent mistake in your u-factoring.
u^2 -11u + 24
= (u - 3)(u - 8)
= (x-2)(x-7)
To check if your answer is correct, we need to go through the steps of u-substitution. Here's how you can do that:
1. Start with the equation:
u^2 - 11u + 24
2. Substitute x + 1 = u. This will give you:
(x + 1)^2 - 11(x + 1) + 24
Expanding this equation, you will get:
(x^2 + 2x + 1) - 11x - 11 + 24
Simplifying further:
x^2 + 2x + 1 - 11x - 11 + 24
Combining like terms:
x^2 - 9x + 14
3. Now you need to factorize this quadratic equation:
The factors of 14 that add up to -9 are -2 and -7. So the factored equation becomes:
(x - 2)(x - 7)
Therefore, the correct factored form is (x - 2)(x - 7), not (x + 4)(x - 7) as you wrote.