ANSWER:
No, x + 2 is not a factor of x³–x²–5x–3.
EXPLANATION:
We can check this using the factor theorem.
"The factor theorem states that a polynomial f(x) has a factor (x - k) if and only if f(k)=0 (i.e. k is a root)."
In the problem,
- (x - k) —> x + 2 | k = -2
- f(x) = x³–x²–5x–3
Sove for f(k).
- f(x) = x³–x²–5x–3
- f(k) = k³ - k² - 5k - 3
- f(-2) = (-2)³ - (-2)² - 5(-2) - 3
- f(-2) = -8 - 4 + 10 - 3
- f(-2) = -12 + 10 - 3
- f(-2) = -5
- f(k) = -5
- f(k) is not equal to 0 so x + 2 is not a factor of x³–x²–5x–3.
- (-5 is the remainder.)
