Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer and a_n ≠ 0.

Front

What are the zeros of a polynomial function?

Back

The zeros of a polynomial function are the values of x for which the function f(x) equals zero. They are also known as the roots of the polynomial.

Tags

CCSS.HSF-IF.C.7C

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the function equal to zero and solve for x. This can involve factoring, using the quadratic formula, or applying numerical methods.

Tags

CCSS.HSF-IF.C.7C

Front

What is the maximum number of zeros a polynomial function can have?

Back

The maximum number of zeros a polynomial function can have is equal to its degree. For example, a polynomial of degree n can have at most n zeros.

Front

What is the minimum number of zeros a polynomial function can have?

Back

The minimum number of zeros a polynomial function can have is zero. A polynomial can have no real roots, especially if it does not cross the x-axis.

Front

What is the relationship between the degree of a polynomial and its graph?

Back

The degree of a polynomial affects the shape of its graph. Higher degree polynomials can have more complex shapes, including multiple turns and intersections with the x-axis.

Front

What is a turning point in the context of polynomial functions?

Back

A turning point is a point on the graph of a polynomial function where the graph changes direction from increasing to decreasing or vice versa. The maximum number of turning points is one less than the degree of the polynomial.

Front

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

Back

The leading coefficient determines the end behavior of the polynomial function's graph. If it is positive, the graph rises to the right; if negative, it falls to the right.

Front

How do you determine the number of turning points in a polynomial function?

Back

The maximum number of turning points in a polynomial function is equal to the degree of the polynomial minus one.

Front

What is synthetic division and when is it used?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor. It is quicker and easier than traditional long division.

Tags

CCSS.HSA.APR.D.6