use the factor theorem to determine whether x-c is a factor of f(x)=x^3+8x^2-18x+20; x-10.
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To determine whether x - c is a factor of f(x) = x^3 + 8x^2 - 18x + 20, we need to see if f(c) = 0.
In this case, we want to determine if x - 10 is a factor. So, we substitute c = 10 into f(x) and see if it equals zero.
f(10) = (10)^3 + 8(10)^2 - 18(10) + 20
Simplifying this expression, we have:
f(10) = 1000 + 800 - 180 + 20
f(10) = 1640
Since f(10) is not equal to zero, we can conclude that x - 10 is not a factor of f(x).
To use the factor theorem to determine whether x-c is a factor of f(x), we need to evaluate f(c) and check if it equals zero.
In this particular case, we are given f(x) = x^3 + 8x^2 - 18x + 20 and we need to determine whether x - c is a factor of f(x), where c = 10.
1. Substitute c into the polynomial f(x). Replace x with c in the expression f(x).
f(c) = c^3 + 8c^2 - 18c + 20
2. Evaluate the expression f(c) by simply plugging in the value of c.
f(10) = 10^3 + 8(10)^2 - 18(10) + 20
f(10) = 1000 + 800 - 180 + 20
f(10) = 1640
3. Check if f(c) equals zero. If f(c) equals zero, then x - c is a factor of f(x). Otherwise, it is not.
Since f(10) = 1640 and 1640 is not equal to zero, we can conclude that x - 10 is not a factor of f(x).
In summary, after substituting x with 10 in the polynomial f(x) = x^3 + 8x^2 - 18x + 20 and evaluating the expression, we found that f(10) = 1640, which is not equal to zero. Therefore, x - 10 is not a factor of f(x).