How can you determine whether a linear binomial is a factor of a polynomial without using the remainder theorem?

Answers 2

A linear binomial is a factor of a polynomial if the polynomial value is 0 at the zeros of the linear binomial

How to determine the factor?Assume a polynomial function is

P(x) = (x - 3)(x + 1)(x -2)

And a linear binomial is:

x - 3 = 0

We start by calculating the value of x in x - 3 = 0

x = 3

Next, we substitute x = 3 in P(x) = (x - 3)(x + 1)(x -2)

P(3) = (3 - 3)(3 + 1)(3 -2)

Evaluate

P(3) = 0

Since P(3) = 0, then the linear binomial x - 3 is a factor of P(x) = (x - 3)(x + 1)(x -2)

AI generated Answer

Quick answer: You can determine whether a linear binomial is a factor of a polynomial by using synthetic division. Full explanation: Synthetic division is a method for quickly dividing a polynomial by a linear binomial such as x-a. It allows you to determine whether the linear binomial is a factor of the polynomial without using the remainder theorem. If the result of the synthetic division is zero, then the linear binomial is a factor of the polynomial.
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