Add, Subtract, and Multiply 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, which are terms that have the same variable raised to the same power. For example, (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves distributing the negative sign and then combining like terms. For example, (3x^2 + 2x) - (x^2 + 4) = 2x^2 + 2x - 4.

Front

How do you multiply two polynomials?

Back

To multiply two 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, 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 polynomial. For example, in the polynomial 4x^3 + 2x^2 + 5, the degree is 3.

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms. For example, 3x + 4 is a binomial.

Front

What is a trinomial?

Back

A trinomial is a polynomial that contains exactly three terms. For example, x^2 + 5x + 6 is a trinomial.

Front

What is the result of multiplying (b + 3)(b^2 + 2b + 1)?

Back

The result is b^3 + 5b^2 + 7b + 3.

Front

What is the result of simplifying 5(3x + 2)?

Back

The result is 15x + 10.

Front

What is the result of subtracting (5x^4 - 4x^3 - 2x^2 + x - 19) - (x^4 + 5x^3 + 8x^2 + x + 5)?

Back

The result is 4x^4 - 9x^3 - 10x^2 - 24.