This page presents practice questions on the degree of a polynomial and the zeros (roots) of a polynomial with their multiplicities. Complete solutions are provided at the bottom of the page. For additional practice, see our polynomial problem collection.
What is the degree of the polynomial \(P\) defined by
\[ P(x) = 2x - 2? \]What is the degree of the polynomial \(P\) defined by
\[ P(x) = 2(x - 2)(x^2 + 5)? \]What is the degree of the polynomial \(P\) defined by
\[ P(x) = -5(x - 2)(x^3 + 5) + x^5? \]Give the zeros of the polynomial \(P\) and list their multiplicities:
\[ P(x) = (x + 2)(x - 1) \]Give the zeros of the polynomial \(P\) and list their multiplicities:
\[ P(x) = (x - 2)^2(x + 4) \]Give the zeros of the polynomial \(P\) and list their multiplicities:
\[ P(x) = (x + 5)^3(x - 6)(-x + 6) \]Give the zeros of the polynomial \(P\) and list their multiplicities:
\[ P(x) = (x + 1)(x + 2) + (x + 1)(x + 2)^2 \]Give the zeros of the polynomial \(P\) and list their multiplicities:
\[ P(x) = (x - 4)(x^2 + 4)^2 \]Give the zeros of the polynomial \(P\) and list their multiplicities:
\[ P(x) = (-x + 3)(x^2 + 2x + 5)^2 \]Give the zeros of the polynomial \(P\) and list their multiplicities:
\[ P(x) = -x(-x - 2)^2(x + 2) \]1) Degree \(= 1\)
2) Degree \(= 3\)
3) Degree \(= 5\)
4) Zeros: \[ x = -2 \text{ (multiplicity 1)}, \quad x = 1 \text{ (multiplicity 1)} \]
5) Zeros: \[ x = 2 \text{ (multiplicity 2)}, \quad x = -4 \text{ (multiplicity 1)} \]
6) Zeros: \[ x = -5 \text{ (multiplicity 3)}, \quad x = 6 \text{ (multiplicity 2)} \]
7) Zeros: \[ x = -1,\; x = -2,\; x = -3 \quad \text{(each with multiplicity 1)} \]
8) Zeros: \[ x = 4 \text{ (multiplicity 1)}, \quad x = 2i \text{ (multiplicity 2)}, \quad x = -2i \text{ (multiplicity 2)} \]
9) Zeros: \[ x = 3 \text{ (multiplicity 1)}, \quad x = -1 + 2i \text{ (multiplicity 2)}, \quad x = -1 - 2i \text{ (multiplicity 2)} \]
10) Zeros: \[ x = 0 \text{ (multiplicity 1)}, \quad x = -2 \text{ (multiplicity 3)} \]