Adding and Subtracting 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 like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms, while 3x and 3x^2 are not.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients while keeping the variable part the same.

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 4x^3 - 5x^2 + 3x, the degree is 3.

Front

What is the coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in 4x^3, 4 is the coefficient.

Front

What does it mean to combine like terms?

Back

Combining like terms means to simplify an expression by adding or subtracting the coefficients of terms that have the same variable and exponent.

Front

What is the result of adding (4x^3 - 5x^2 + 3x) and (-2x^3 - x^2 + 6x)?

Back

The result is 2x^3 - 6x^2 + 9x.

Front

How do you simplify the expression (5x + 2) + (4x + 5)?

Back

You simplify it by combining like terms to get 9x + 7.

Front

What is the sum of (3x + 7) and (6x + 7)?

Back

The sum is 9x + 14.

Front

What is the simplified form of (9x + 11) + (x - 3)?

Back

The simplified form is 10x + 8.