Question

If g(t) = 13t^3 + 15t^2 - 31t + 37, use synthetic division to find g(-2).

Answer 1

To find g(-2) using synthetic division, divide the coefficients of the polynomial function g(t) = 13t^3 + 15t^2 - 31t + 37 by -2 using synthetic division.

Step-by-step explanation:

To find g(-2) using synthetic division, we will use the coefficients of the polynomial function g(t) = 13t^3 + 15t^2 - 31t + 37. We will use -2 as the synthetic division divisor.

First, write down the coefficients of the polynomial in descending order: 13, 15, -31, 37.

Use synthetic division to divide the coefficients by -2:

13 15 -31 37
-2 |-26 22 18 -30
-12 -61 - 34
-69 37

The remainder obtained using synthetic division is 37. Therefore, g(-2) = 37.