Question

Use synthetic substitution to find g(3) and g(-6) for the function g(x)=x^5-5x^3-10x+4

Answer 1

g(3)=82

g(-6)=-6632

Explanation:

To find g(3) we are going to use synthetic division for dividing the polynomial x^5-5x^3-10x+4 by x-3.

So this means 3 goes on the outside.

Also since we are missing x^4 and x^2 term, we will need to put a 0 placeholders there.

3 | 1 0 -5 0 -10 4

| 3 9 12 36 78

|_____________________

1 3 4 12 26 82

So g(3)=82

To find g(-6) we will put -6 on the outside:

-6 | 1 0 -5 0 -10 4

| -6 36 -186 1116 -6636

--------------------------------------

1 -6 31 -186 1106 -6632

So g(-6)=-6632