Adding, Subtracting and Multiplying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What are the degrees of polynomials?

Back

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

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (3x^2 + 2x) + (4x^2 + 5) = 7x^2 + 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 - 3) - (2x^2 + 1) = 3x^2 - 4.

Front

What is the product of two binomials?

Back

The product of two binomials can be found using the distributive property or the FOIL method. For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

What is the FOIL method?

Back

FOIL stands for First, Outside, Inside, Last. It is a method used to multiply two binomials. For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6.

Front

What is a like term?

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

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, and 3x + 2 is a polynomial.

Front

How do you multiply a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term in the polynomial. For example, 2x(3x^2 + 4x) = 6x^3 + 8x^2.

Front

What is the result of (x + 1)(x - 1)?

Back

The result is x^2 - 1, which is a difference of squares.