Classifying, Adding, Subtracting, Multiplying 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

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (3x^2 + 2x) + (4x^2 + 3) = (3 + 4)x^2 + (2)x + (3) = 7x^2 + 2x + 3.

Front

What are like terms in polynomials?

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, while 3x^2 and 4x are not.

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 + 7, the degree is 3.

Front

How do you subtract polynomials?

Back

To subtract polynomials, change the sign of the terms in the polynomial being subtracted and then combine like terms. For example, (3x + 5) - (2x - 3) = 3x + 5 - 2x + 3 = (3 - 2)x + (5 + 3) = x + 8.

Front

What is the product of two polynomials?

Back

The product of two polynomials is found by multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms. For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

Front

What is the FOIL method?

Back

The FOIL method is a technique for multiplying two binomials. It stands for First, Outside, Inside, Last, referring to the order in which you multiply the terms. For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

What does it mean to combine like terms?

Back

Combining like terms means to add or subtract coefficients of terms that have the same variable and exponent. For example, in 2x + 3x, you combine to get 5x.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, 3x + 4 is a binomial.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. For example, x^2 + 5x + 6 is a trinomial.