Zeros, Factors and Writing Polynomial Functions

Front

What are the zeros of a polynomial function?

Back

The zeros (or roots) of a polynomial function are the values of x for which the function equals zero.

Front

How do you factor a polynomial?

Back

To factor a polynomial, you express it as a product of its factors, which can include numbers, variables, or other polynomials.

Front

What is the relationship between zeros and factors of a polynomial?

Back

If x = a is a zero of a polynomial, then (x - a) is a factor of that polynomial.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written as a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0.

Front

How do you find the roots of a polynomial equation?

Back

To find the roots, set the polynomial equal to zero and solve for x using factoring, the quadratic formula, or other methods.

Front

What is a cubic polynomial?

Back

A cubic polynomial is a polynomial of degree three, which can be expressed in the form ax^3 + bx^2 + cx + d.

Front

What does it mean to write a polynomial in factored form?

Back

Writing a polynomial in factored form means expressing it as a product of its linear factors.

Front

How do you determine the degree of a polynomial?

Back

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

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree and determines the end behavior of the polynomial graph.

Front

What is the Factor Theorem?

Back

The Factor Theorem states that if f(c) = 0 for a polynomial f(x), then (x - c) is a factor of f(x).