Final answer:
The binomial x-1 is a factor of the polynomial x^3 + 8x^2 + 11x - 20 because substituting x = 1 into the polynomial yields zero, confirming it by the Remainder Theorem.
Step-by-step explanation:
The question asks whether the binomial x-1 is a factor of the polynomial x^3 + 8x^2 + 11x - 20. To determine if the binomial is a factor, we can use synthetic division or the Remainder Theorem. The Remainder Theorem states that if you divide a polynomial by a binomial of the form x - c, the remainder is equal to the value of the polynomial for x = c. So in this case, we can substitute x = 1 into the polynomial and check if the result is zero.
To substitute x = 1 into the polynomial:
1^3 + 8(1)^2 + 11(1) - 20 = 1 + 8 + 11 - 20 = 0
Since the result is zero, this confirms that x-1 is indeed a factor of the polynomial x^3 + 8x^2 + 11x - 20.