Math 3 HW3 Polynomial

Front

What is the Complex Conjugate Root Theorem?

Back

If a polynomial has a complex root a + bi, then its complex conjugate a - bi is also a root.

Front

Given a complex root 3 + 5i, what is its complex conjugate?

Back

3 - 5i

Front

What does the Rational Root Theorem state?

Back

The Rational Root Theorem provides a way to find all possible rational roots of a polynomial equation.

Front

What are the possible rational zeros of a polynomial?

Back

The possible rational zeros are the factors of the constant term divided by the factors of the leading coefficient.

Front

How do you find the zeros of a polynomial?

Back

To find the zeros, set the polynomial equal to zero and solve for x.

Front

What is a y-intercept?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, found by evaluating the function at x = 0.

Front

What are x-intercepts?

Back

X-intercepts are the points where the graph of a function crosses the x-axis, found by setting the function equal to zero.

Front

Is the function f(x) = x^2 + 1 a function?

Back

Yes, it is a function because for every x-value, there is exactly one y-value.

Front

Is the relation {(1,2), (2,3), (1,4)} a function?

Back

No, it is not a function because the input 1 corresponds to two different outputs (2 and 4).

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.