I used the U-subsitution
(x + 1)^2 - 11 (x + 1) + 24
u^2 - 11u +24
(u + 3) (u - 8) should this be (u - 3)?
(x + 1 + 3) (x + 1 - 8)
(x + 4) (x - 7) or should it be (x - 2)
Can anyone explain which is the correct answer
thanks
(x + 1)^2 - 11 (x + 1) + 24
u^2 - 11u +24
(u + 3) (u - 8) should this be (u - 3)?
Yes, both signs are negative.
(x+1-3)(x+1-8)
(x-2)(x-7)
Thanks
To solve the expression using u-substitution, you correctly substituted u for (x + 1):
(x + 1)^2 - 11(x + 1) + 24 becomes u^2 - 11u + 24
You then factored the quadratic expression u^2 - 11u + 24. However, there seems to be a mistake in your factorization. Let's correct it:
u^2 - 11u + 24 can be factored as (u - 3)(u - 8)
Now, substitute back in the original variable x:
(x + 1 + 3)(x + 1 - 8) becomes (x + 4)(x - 7)
So, the correct factorization is (x + 4)(x - 7).
It seems you were confused regarding the signs. In the factorization, we have (u - 3) and (u - 8), not (u + 3) and (u - 8). Similarly, when substituting back, we obtain (x + 4)(x - 7), not (x + 4)(x - 2).