use the factor theorem to determine whether x-c is a factor of f(x)
f(x)=x^3+8x^2-18x+20; x-10
I have a doubt in my answer, i determined that x-10 is not a factor... am i right? please verify as my exam is tomorrow night at college. thank you for your time and hard work:)
It can be shown that x-10 is not a factor of x^3+8x^2-18x+20. So your are correct.
If you wish, you could try (x+10) and show that it is a factor of x^3+8x^2-18x+20.
thank you so much dear mate, yes i took your advise and indeed i got it as a factor:) thank you.
You're welcome!
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To determine whether x - c is a factor of f(x), we can use the factor theorem. According to the factor theorem, if (x - c) is a factor of f(x), then f(c) = 0.
In this case, f(x) = x^3 + 8x^2 - 18x + 20, and x - 10 is the factor we want to test. So, we need to check if f(10) equals 0.
To calculate f(10), substitute x with 10 in the equation:
f(10) = 10^3 + 8(10^2) - 18(10) + 20
= 1000 + 8(100) - 180 + 20
= 1000 + 800 - 180 + 20
= 1640
Since f(10) is not equal to 0 (it's equal to 1640), we can conclude that x - 10 is not a factor of f(x).
So, your answer is correct! x - 10 is not a factor of f(x).
Good luck on your exam tomorrow!