ANSWER:
Yes, x+3 is a factor of x⁴ +4x³+x²–6x.
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 + 3 | k = -3
- f(x) = x⁴ +4x³+x²–6x
Sove for f(k).
- f(x) = x⁴ +4x³+x²–6x
- f(k) = k⁴ + 4k³ + k² - 6k
- f(-3) = (-3)⁴ + 4(-3)³ + (-3)² - 6(-3)
- f(-3) = 81 - 108 + 9 + 18
- f(-3) = 0
- f(k) = 0
- f(k) is equal to 0 so that means x+3 is a factor of x⁴ +4x³+x²–6x.
