Question

x + 1 is a factor of the polynomial​

Answer 1

Answer:

Using factor theorem x + 1 = 0. Let p(x) = (x^3 + x^2 - x - 1). Therefore, (x + 1) is a factor of (x^3 + x^2 - x - 1).

Answer 2

Use the Factor Theorem to determine whether x – 1 is a factor of

    f (x) = 2x4 + 3x2 – 5x + 7.

For x – 1 to be a factor of  f (x) = 2x4 + 3x2 – 5x + 7, the Factor Theorem says that x = 1 must be a zero of  f (x). To test whether x – 1 is a factor, I will first set x – 1 equal to zero and solve to find the proposed zero, x = 1. Then I will use synthetic division to divide f (x) by x = 1. Since there is no cubed term, I will be careful to remember to insert a "0" into the first line of the synthetic division to represent the omitted power of x in 2x4 + 3x2 – 5x + 7:

completed division: 2  2  5  0  7

Since the remainder is not zero, then the Factor Theorem says that:

x – 1 is not a factor of f (x).