Question

Use the polynomial function

p(x) = 2x3 + 5x2 - x - 6 to answer questions 2, 3 and 4 below.
Show that (x - 1) is a factor of (x) using the Remainder Theorem.

Answer 1

To show that (x - 1) is a factor of the polynomial function p(x) = 2x^3 + 5x^2 - x - 6, we can use the Remainder Theorem.

Step-by-step explanation:

To show that (x - 1) is a factor of the polynomial function p(x) = 2x^3 + 5x^2 - x - 6, we can use the Remainder Theorem. According to the Remainder Theorem, if (x - a) is a factor of a polynomial function, then the remainder when the polynomial is divided by (x - a) is equal to zero. So, to prove that (x - 1) is a factor of p(x), we need to show that p(1) = 0.

Substituting x = 1 into p(x), we get:

p(1) = 2(1)^3 + 5(1)^2 - 1 - 6

= 2 + 5 - 1 - 6

= 0

Since p(1) equals zero, we can conclude that (x - 1) is a factor of p(x).