Final answer:
To test if x+3 is a factor of x³+6x²+5x-11, we substitute x=-3 into the polynomial and find that it does not equal zero. Therefore, x+3 is not a factor of the polynomial.
Step-by-step explanation:
To determine if the binomial x+3 is a factor of the polynomial x³+6x²+5x-11, we can apply the factor theorem, which states that if you can substitute the value of 'x' that makes the binomial equal to zero and the polynomial equals zero, then the binomial is indeed a factor of the polynomial.
The binomial x+3 is equal to zero when x = -3. Substituting -3 into the polynomial, we get:
(-3)³ + 6(-3)² + 5(-3) - 11 = -27 + 54 - 15 - 11 = 16.
Since the result is not zero, the binomial x+3 is not a factor of the polynomial x³+6x²+5x-11.