Consider the graph of the polynomial function p(x). Given that (2x+3) is a factor of p(x), which of the following could be the multiplicity of (2x+3)?

Question

(1 point)

−1.5

1

1.5

2

Answer 1

The multiplicity of a factor in a polynomial function represents the number of times that factor is repeated.

If (2x+3) is a factor of p(x), it means that when we divide p(x) by (2x+3), the remainder is 0.

Let's consider each option:

-1.5: The multiplicity cannot be negative or a decimal number.

1: The multiplicity can be 1. If the factor (2x+3) appears once in the function, it means that there is one root at x = -3/2.

1.5: The multiplicity cannot be a decimal number.

2: The multiplicity can also be 2. If the factor (2x+3) appears twice in the function, it means that there is a double root at x = -3/2.

So, the possible multiplicities for (2x+3) are 1 and 2. The correct option is 2.