Add, Subtract and Multiply Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication. Example: 3x^2 + 2x - 5.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power. Example: (2x^2 + 3x) + (4x^2 + 2) = 6x^2 + 3x + 2.

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves changing the signs of the terms in the polynomial being subtracted and then combining like terms. Example: (5x^2 + 4) - (2x^2 + 3) = 3x^2 + 1.

Front

How do you multiply two polynomials?

Back

To multiply polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial. Example: (x + 2)(x + 3) = x^2 + 5x + 6.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression. Example: In 4x^3 + 2x^2 - x, the degree is 3.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. Example: 3x + 4.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. Example: x^2 + 5x + 6.

Front

What is the result of multiplying (2n + 2)(6n + 1)?

Back

12n^2 + 14n + 2.

Front

What is the result of multiplying (4x + 3)(2x - 1)?

Back

8x^2 + 2x - 3.

Front

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

Back

-2x^2 + 11x - 4.