Up to 5-2 Factored Form and zeros of Polynomials

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its factors, which can include linear factors and constants.

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for the variable.

Front

What is a cubic polynomial?

Back

A cubic polynomial is a polynomial of degree three, which can be expressed in the form f(x) = ax^3 + bx^2 + cx + d, where a ≠ 0.

Front

What does the leading coefficient of a polynomial indicate?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial, and it determines the end behavior of the polynomial's graph.

Front

How do you factor a polynomial?

Back

To factor a polynomial, look for common factors, use grouping, or apply special factoring techniques such as the difference of squares or the quadratic formula.

Front

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

Back

X-intercepts are the points where the graph of the polynomial crosses the x-axis, and they correspond to the zeros of the polynomial.

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have up to n real zeros, counting multiplicities.

Front

What is the process for adding polynomials?

Back

To add polynomials, combine like terms by adding their coefficients while keeping the same variable and exponent.

Front

What is the factored form of a polynomial with x-intercepts at x = 1 and x = -2?

Back

The factored form is (x - 1)(x + 2).

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms, typically as ax^n + bx^(n-1) + ... + k.