Answer:
C. -13
Step-by-step explanation:
The polynomial f(x) she is dividing would be f(x)=1x²-7x-3. This is because in synthetic division, the numbers used are the coefficients of the polynomial, and the polynomial will have a degree one larger than the divisor. Since the divisor is x-2, with a degree of 1, the polynomial will have a degree of 2, meaning it begins with an x².
The first coefficient is 1; this is 1x². The second coefficient is -7; this is -7x. The last coefficient is -3; this is -3. Together, this gives us
f(x) = 1x²-7x-3
To find f(2), substitute 2 in for every x:
f(2) = 1(2²)-7(2)-3 = 1(4)-14-3 = 4-14-3 = -10-3 = -13
