Operations with Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 3x^2 + 2x - 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.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It is used to multiply a single term by a sum or difference.

Front

How do you multiply two binomials?

Back

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

Front

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

Back

The result is x^2 + x - 6.

Front

What is the formula for the area of a rectangle?

Back

The area of a rectangle is calculated by multiplying its length by its width: Area = length × width.

Front

How do you find the area of a rectangle with length (x - 5) and width (3x + 1)?

Back

Area = (x - 5)(3x + 1) = 3x^2 - 14x - 5.

Front

What is the square of a binomial?

Back

The square of a binomial (a + b)^2 is equal to a^2 + 2ab + b^2.

Front

What is the result of (x + 7)^2?

Back

The result is x^2 + 14x + 49.

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.