Solving Polynomial Equations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What does it mean for a polynomial to have zeros?

Back

Zeros of a polynomial are the values of the variable that make the polynomial equal to zero. They are also known as roots or x-intercepts.

Front

How many zeros does the polynomial function P(x) = 3x^4 + 4x - 8 have?

Back

4

Front

What are the x-intercepts of the polynomial y = 3(x + 4)(x + 1)(x - 3)?

Back

-4, -1, 3

Front

What is another way to say 'where a function crosses the x-axis'?

Back

x-intercept, zero, root, all of these.

Front

Find all zeros of the polynomial function P(x) = x^3 + 6x^2 + 9x + 54.

Back

-6, 3i, -3i

Front

What is the degree of the polynomial P(x) = 3x^4 + 4x - 8?

Back

4

Front

What is the leading coefficient of the polynomial P(x) = 3x^4 + 4x - 8?

Back

3

Front

What does the Fundamental Theorem of Algebra state?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root.

Front

What is synthetic division used for?

Back

Synthetic division is a simplified method for dividing a polynomial by a linear binomial.