Add and Subtract 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 the polynomial 4x^3 + 2x^2 - x + 5, 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) + (4x + 5) = (3x + 4x) + (2 + 5) = 7x + 7.

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

How do you subtract polynomials?

Back

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

Front

What is the result of (a + b) + c?

Back

The result of (a + b) + c is the same as a + (b + c) due to the associative property of addition.

Front

What is the result of (a - b) - c?

Back

The result of (a - b) - c is not necessarily equal to a - (b + c). It is important to distribute the negative sign correctly.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a parenthesis.

Front

How do you simplify the expression (4x^2 + x) - (x^2 + 2x)?

Back

To simplify, distribute the negative sign: (4x^2 + x) - (x^2 + 2x) = 4x^2 + x - x^2 - 2x = (4x^2 - x^2) + (x - 2x) = 3x^2 - x.

Front

What is the sum of (5x + 2) + (4x + 5)?

Back

The sum is (5x + 2) + (4x + 5) = (5x + 4x) + (2 + 5) = 9x + 7.