Simplifying Polynomials (Combining Like Terms)

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 combine like terms in a polynomial?

Back

To combine like terms, add or subtract the coefficients of the terms that have the same variable and exponent.

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 the coefficient in a polynomial term?

Back

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

Front

Simplify the polynomial: 3a + 4b - 2a + 5b.

Back

The simplified polynomial is a + 9b.

Front

What is the result of simplifying the expression: 6x^2 - 2x + 3x^2 + 4?

Back

The simplified expression is 9x^2 - 2x + 4.

Front

Identify the like terms in the expression: 7y^2 + 3y - 2y^2 + 5.

Back

The like terms are 7y^2 and -2y^2, which combine to form 5y^2.

Front

What is the process of simplifying a polynomial called?

Back

The process of simplifying a polynomial by combining like terms is called polynomial simplification.

Front

What is the difference between a monomial, binomial, and trinomial?

Back

A monomial has one term, a binomial has two terms, and a trinomial has three terms.