Polynomial Operations

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. Example: 3x^2 + 2x - 5.

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 the polynomial 4x^3 + 2x^2 - x + 7, the degree is 3.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 5x^4 + 3x^2 - 2, the leading coefficient is 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 + 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. Example: (5x^2 + 3) - (2x^2 + 4) = 3x^2 - 1.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. Example: (a + b)(c + d) = ac + ad + bc + bd.

Front

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

Back

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

Front

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

Back

The sum is 6x^2 + 3x + 5.

Front

What is the difference of (3y^2 + 2) - (y^2 + 4)?

Back

The difference is 2y^2 - 2.

Front

What is the product of (3r - 4)(7r - 5)?

Back

The product is 21r^2 - 43r + 20.