Question

State if the given binomial is a factor of the given polynomial.

(a^3-19a^2+88a+25) +(a-9)
a) Yes
b) No

Answer 1

To determine if the given binomial is a factor of the given polynomial, perform polynomial division and check if the remainder is zero. In this case, the given binomial is not a factor.

Step-by-step explanation:

To determine if the given binomial is a factor of the given polynomial, we can perform polynomial division. We divide the given polynomial by the given binomial and check if the remainder is zero. If the remainder is zero, then the binomial is a factor, otherwise it is not.

In this case, we perform polynomial division: (a^3-19a^2+88a+25) ÷ (a-9). The quotient is a^2 - 10a - 7 and the remainder is 88. Since the remainder is not zero, the given binomial (a-9) is not a factor of the given polynomial.