Combining Polynomials (Add, Sub, Mult)

Front

What is a polynomial?

Back

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

Front

What does it mean to combine polynomials?

Back

Combining polynomials involves adding, subtracting, or multiplying polynomial expressions to simplify or find a new polynomial.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x + 3) + (4x + 5) = 6x + 8.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degree. For example, 4x^3 + 2x^2 - x + 7.

Front

What is a leading coefficient?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 3x^4 + 2x^3 - x, the leading coefficient is 3.

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, the degree of 5x^3 + 2x^2 - 4 is 3.

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property (FOIL for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

Front

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

Back

The result is x^2 + 5x + 6.

Front

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

Back

The result is 4x^2 + 12x + 9.