Question

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f.

k = -1; f(x) = 4x3 - 2x2 + 2x + 4; Lower bound?
 Yes or no?

Answer 1

Hello,

The divisors of 4/4 are 1 or -1

Answer Yes

Answer 2

Yes

Explanation:

Given the polynomial

f(x) = 4x³ - 2x² + 2x + 4

we are asked to use synthetic division to divide f(x) by (x - k) where k = -1. This is performed as follows:

-1 | 4 -2 2 4

| -4 6 -8

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

4 -6 8 -4

Given that k < 0 and the values in the bottom row of the synthetic division alternate between non-negative and non-positive, then x = -1 is a lower bound for the real zeros of the function f(x).