I need someone to check this to see if I am doing it correctly.
k^3+k
k^2+k-42
k(k^2+1)
(k+7)(k+6)
k=-7 k=6
(-0,-7)(-7,6)
(6,0)
Leaving aside the virtually impenetrable formatting, your math appears to be ok.
Hello Steve
Why do you have to be so sarcastic to those who are seeking help? If you couldn't understand what I wrote, then how could you tell my math was ok?
because I have been exposed to similar careless mistakes displayed by others.
Tell me. Just looking at your posting, could you easily tell what was being asked? The questions and solutions are all mixed up together.
To check whether your calculations are correct, you can substitute the values of k (-7 and 6) into the given expressions and simplify.
Let's start with the expression k^3 + k:
Substituting k = -7:
(-7)^3 + (-7) = -343 - 7 = -350
Substituting k = 6:
(6)^3 + 6 = 216 + 6 = 222
Next, let's check the expression k^2 + k - 42:
Substituting k = -7:
(-7)^2 + (-7) - 42 = 49 - 7 - 42 = 0
Substituting k = 6:
(6)^2 + 6 - 42 = 36 + 6 - 42 = 0
So, it seems that you have calculated both expressions correctly.
Moving on to the next part of your answer, which is the factorization of the expression k(k^2 + 1), you correctly factored it as (k + 7)(k + 6).
Now, let's determine the x-intercepts by setting k = -7 and k = 6:
When k = -7:
(-7 + 7)(-7 + 6) = (0)(-1) = 0
When k = 6:
(6 + 7)(6 + 6) = (13)(12) = 156
Hence, the x-intercepts are (-7, 0) and (6, 0).
Overall, it looks like your calculations are correct!