Polynomials Review

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers, combined using addition, subtraction, and multiplication.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 5x^3 - 6x + 1, the degree is 3.

Front

What is standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 9x^3 + 8x^2 - 3x - 11 is in standard form.

Front

How do you find the difference of two polynomials?

Back

To find the difference of two polynomials, subtract the corresponding coefficients of like terms. For example, (3 - 2x + 2x^2) - (4x - 5 + 3x^2) results in -x^2 - 6x + 8.

Front

What is the factored form of x^3 + y^3?

Back

The factored form of x^3 + y^3 is (x + y)(x^2 - xy + y^2).

Front

What is a relative maximum in a polynomial function?

Back

A relative maximum is a point on the graph of a polynomial function where the function value is higher than the values of the function at nearby points.

Front

What is a relative minimum in a polynomial function?

Back

A relative minimum is a point on the graph of a polynomial function where the function value is lower than the values of the function at nearby points.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 4x^3 + 2x^2 - 5, the leading coefficient is 4.

Front

What is the difference between linear, quadratic, cubic, and quartic polynomials?

Back

Linear polynomials have a degree of 1, quadratic polynomials have a degree of 2, cubic polynomials have a degree of 3, and quartic polynomials have a degree of 4.

Front

What is the sum of two polynomials?

Back

To find the sum of two polynomials, add the corresponding coefficients of like terms. For example, (2x^2 + 3x) + (4x^2 - 2x) results in 6x^2 + x.