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 does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions to form a new polynomial.

Front

What are like terms in polynomials?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3y^2 and 5y^2 are like terms.

Front

How do you subtract polynomials?

Back

To subtract polynomials, you change the signs of the terms in the polynomial being subtracted and then combine like terms.

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

Front

What is the sum of (3y^2 + y^3 - 5) and (4y^2 - 4y + 2y^3 + 8)?

Back

The sum is 3y^3 + 7y^2 - 4y + 3.

Front

What is the result of (2x^2 + 5x - 7) + (3 - 4x^2 + 6x)?

Back

The result is -2x^2 + 11x - 4.

Front

How do you simplify (6x + 4x^4 - 3x^2) + (7x^4 + 5x^2 + 8x)?

Back

The simplified expression is 11x^4 + 2x^2 + 14x.

Front

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

Back

The difference is -x^2 - 6x + 8.

Front

What does it mean to simplify an expression?

Back

Simplifying an expression means to combine like terms and reduce the expression to its simplest form.