Final answer:
To determine if a linear binomial factors of a polynomial P(x), we need to check if P(x) can be divided evenly by the linear binomial. This can be done by performing polynomial long division or using the remainder theorem.
Step-by-step explanation:
A linear binomial is a binomial expression in which the degree of each term is 1. In other words, it is an expression of the form ax + b, where a and b are constants. To determine if a linear binomial factors of a polynomial P(x), we need to check if P(x) can be divided evenly by the linear binomial. This can be done by performing polynomial long division or using the remainder theorem.
For example, suppose we have the polynomial P(x) = 2x^2 + 3x - 4 and the linear binomial x + 2. To check if x + 2 factors of P(x), we divide P(x) by x + 2 using polynomial long division:
(2x^2 + 3x - 4) ÷ (x + 2)
We perform the division and check if the remainder is zero. If the remainder is zero, then x + 2 is a factor of P(x). Otherwise, it is not a factor.