Answer:
Fourth option ([tex]f(-3)=36[/tex])
Step-by-step explanation:
The complete exercise is: "Cristoble used synthetic division to divide the polynomial f(x) by [tex]x + 3[/tex], as shown on the table. What is the value of f(−3).
A synthetic division setup with respective columns containing the following numbers: column 1 containing -3 as the divisor, column 2 containing 2, blank and 2, column 3 containing negative 5, negative 6, negative 11, and column 4 containing 3, 33, 36. There is a line above the numbers 2, negative 11 and 36.
-3
2
33
36"
Based on the given description, you can determine that this Synthetic division have the form shown in the image attached.
You know that the polynomial [tex]f(x)[/tex] is divided by [tex]x+3[/tex]
Then, you can identify that the constant of the divisor is:
[tex]a=-3[/tex]
By definition:
1) The numbers located in the first row are the coefficient of the polynomial you are dividing.
2) The first two numbers located in the third row are the coefiicients of the Quotient.
3) The last number of the third row is the Remainder.
Therefore, since the division of the polynomial [tex]f(x)[/tex] by [tex]x+3[/tex] gives a Remainder of [tex]36[/tex], you can conclude that:
[tex]f(-3)=36[/tex]
