Graphing Polynomials Factor the polynomial and use the factored form to find the zeros. Then ske

step 1 So we're going to use the factor by grouping method to factor this polynomial and find the zeros

Graphing Polynomials Factor the polynomial and use the...

Key Concepts

Polynomial Functions

Polynomial functions are mathematical expressions involving variables raised to nonnegative integer powers, combined using addition, subtraction, and multiplication. They form the basis for many algebraic analyses and are characterized by their degree, which indicates the highest power of the variable present, and by their smooth and continuous nature.

Factoring Polynomials

Factoring polynomials is the process of rewriting a polynomial as a product of simpler polynomials or factors. This technique is useful in solving equations, simplifying expressions, and analyzing function behavior, as it often exposes the roots or zeros of the polynomial.

Zero Product Property

The Zero Product Property states that if a product of factors is equal to zero, then at least one of the factors must be zero. This principle is key when solving polynomial equations after factoring, as it allows the determination of the zeros by setting each factor equal to zero.

Zeros of Polynomial Functions

Zeros, or roots, of a polynomial are the values of the variable that make the polynomial equal to zero. They indicate where the graph of the function intersects the x-axis, and finding them is essential for understanding the function’s behavior and for graphing.

Graphing Polynomial Functions

Graphing polynomial functions involves plotting important points, such as zeros and the y-intercept, and analyzing the overall shape of the curve. Additional features include understanding the end behavior based on the leading term and considering the multiplicity of the zeros, which affects how the graph interacts with the x-axis.

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