Operations with polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 3x^2 + 2x - 5 is a polynomial.

Front

What does it mean to simplify a polynomial expression?

Back

Simplifying a polynomial expression means to combine like terms and reduce the expression to its simplest form.

Front

What are like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms.

Front

How do you multiply a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial. For example, -3x^2(7x^2 - x + 4) = -21x^4 + 3x^3 - 12x^2.

Front

What is the area of a rectangle represented by a polynomial?

Back

The area of a rectangle can be found by multiplying its length and width. For example, if length = 2x - 7 and width = 3x, then area = (2x - 7)(3x) = 6x^2 - 21x.

Front

What is the process of subtracting polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (7p + 4p^3 - 8) - (-3p^2 + 2 - 9p) results in 4p^3 + 3p^2 + 16p - 10.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (3x^3 + 3x^2 - 4x + 5) + (x^3 - 2x^2 + x - 4) = 4x^3 + 1x^2 - 3x + 1.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 4x^3 + 2x^2 - x, the degree is 3.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in the term 5x^2, 5 is the coefficient.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, 3x is a monomial, while 3x + 2 is a polynomial.