Adding 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, 3x^2 and 5x^2 are like terms.

Front

How do you combine like terms?

Back

To combine like terms, add or subtract their coefficients while keeping the variable part unchanged. For example, 3x + 5x = 8x.

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 - x, the degree is 3.

Front

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

Back

The sum is 5x^2 - 2y^2.

Front

What is the sum of (-3x + 4) and (8x - 5)?

Back

The sum is 5x - 1.

Front

How do you simplify the expression (4a^3 - 8a - 4a^2) + (7a^3 - 7 - 6a)?

Back

The simplified expression is 11a^3 - 4a^2 - 14a - 7.

Front

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

Back

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

Front

What is the coefficient in the polynomial 5x^2 + 3x - 7?

Back

The coefficients are 5 (for x^2), 3 (for x), and -7 (the constant term).