Roots/Graphs of Polynomials

Front

What is a root of a polynomial?

Back

A root of a polynomial is a value of x for which the polynomial equals zero.

Front

What is another term for the roots of a polynomial?

Back

Zeros, solutions, or x-intercepts.

Front

How do you find the roots of a polynomial function?

Back

Set the polynomial equal to zero and solve for x.

Front

What does the graph of a polynomial function look like at its roots?

Back

The graph intersects the x-axis at the roots.

Front

If f(x) = x^2 - 4, what are the roots?

Back

x = 2 and x = -2.

Front

What is the significance of the x-intercepts in a polynomial graph?

Back

X-intercepts represent the roots of the polynomial.

Front

For the polynomial f(x) = (x + 1)(x - 2), what are the roots?

Back

x = -1 and x = 2.

Front

What is the relationship between the degree of a polynomial and the number of roots?

Back

A polynomial of degree n can have up to n roots.

Front

If f(x) = 2x^3 - 3x^2 + x - 5, how do you determine if x = 1 is a root?

Back

Substitute x = 1 into f(x) and check if f(1) = 0.

Front

What is the Factor Theorem?

Back

If (x - r) is a factor of a polynomial, then f(r) = 0.