A2 Unit 2 Mid Review for Finals

Front

What is the general form of a polynomial function?

Back

A polynomial function is expressed as f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0 and n is a non-negative integer.

Front

What does it mean if a polynomial function has an odd degree?

Back

If a polynomial function has an odd degree, it means that the end behavior of the graph will go in opposite directions: as x approaches positive infinity, f(x) approaches positive infinity, and as x approaches negative infinity, f(x) approaches negative infinity.

Front

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

Back

The x-intercepts (or roots) of a polynomial function are the values of x for which f(x) = 0. They indicate where the graph crosses or touches the x-axis.

Front

What does the multiplicity of a root indicate?

Back

The multiplicity of a root indicates how many times that root is repeated in the polynomial. An odd multiplicity means the graph crosses the x-axis at that root, while an even multiplicity means the graph touches the x-axis but does not cross it.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior of a polynomial function can be determined by the leading term (the term with the highest degree). The sign of the leading coefficient and the degree (odd or even) dictate whether the ends of the graph rise or fall.

Front

What is a linear factor of a polynomial?

Back

A linear factor of a polynomial is an expression of the form (x - r), where r is a root of the polynomial. It represents a point where the polynomial equals zero.

Front

How do you factor a polynomial given one of its roots?

Back

If you know one root (r) of a polynomial, you can factor the polynomial by dividing it by (x - r) using synthetic or long division to find the remaining factors.

Front

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

Back

A polynomial of degree n can have at most n roots, counting multiplicities. This means a cubic polynomial can have up to 3 roots.

Front

What is the difference between a polynomial and a rational function?

Back

A polynomial is a function that consists of terms with non-negative integer exponents, while a rational function is a ratio of two polynomials.

Front

What does it mean for a polynomial to be in standard form?

Back

A polynomial is in standard form when its terms are arranged in descending order of their degrees, from highest to lowest.