Use the Factor Theorem to determine if the given binomial is a factor of the given polynomial function:f(x)=4x^4-20x^3+33x^2-22x+ 5;x-5/2 A:f(-5/2)≠0; the binomial is not a factor of the polynomial

B: f(5/2)≠0; the binomial is not a factor of the polynomial

C:f(-5/2)=0; yes, the binomial is a factor of the polynomial

D: f(5/2)=0; yes, the binomial is a factor of the polynomial

D: f(5/2)=0; yes, the binomial is a factor of the polynomial

Step-by-step explanation:

The easy way to determine is to plug in the potential zero into the polynomial given the binomial divisor and see if it results in 0. If so, then the binomial is a factor of the polynomial:

Because f(5/2)=0, then the binomial is indeed a factor of the polynomial!

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!