Adding Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers, combined using addition, subtraction, and multiplication. For example, 2x^2 + 3x - 5 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions to form a single 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, while 3x^2 and 4x are not.

Front

How do you combine like terms?

Back

To combine like terms, add or subtract their coefficients while keeping the variable part the same. 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 polynomial. For example, in the polynomial 4x^3 + 2x^2 - x, the degree is 3.

Front

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

Back

The sum is x^2 + x + 1.

Front

How do you simplify (2x + 5y - z) + (-6x - 4y + 7z)?

Back

Combine like terms to get -4x + y + 6z.

Front

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

Back

The result is 3x^3 + 5.

Front

How do you combine (5x + 2) and (4x + 5)?

Back

Combine like terms to get 9x + 7.

Front

What is the result of -3(x - 4)?

Back

The result is -3x + 12.