Polynomials and Equations

Question 1

What is a polynomial?

Accepted Answer

An expression made of terms with whole-number powers of a variable, like p(x) = 2x^3 - x + 5. The powers of x must be 0, 1, 2, \ldots

Question 2

What is the degree of a polynomial?

Accepted Answer

The highest power of the variable. For 3x^4 + x^2 - 7, the degree is 4.

Question 3

What does p(2) mean for a polynomial p(x)?

Accepted Answer

The value of the polynomial when x = 2 — substitute 2 for every x and simplify.

Question 4

For p(x) = x^2 + 3x + 1, find p(2).

Accepted Answer

p(2) = 2^2 + 3(2) + 1 = 4 + 6 + 1 = 11.

Question 5

What is a solution of the equation p(x) = 0, and how does it show on the graph of p(x)?

Accepted Answer

A number which makes p(x) = 0. At that number the graph of p(x) crosses (or touches) the x-axis: if p(k) = 0, the point is (k, 0).

Sample questions