Applications of Factoring and Simplifying Rational Expressions

Front

What is the formula for the perimeter of a rectangle?

Back

Perimeter = 2(length + width)

Front

What is the formula for the area of a rectangle?

Back

Area = length × width

Front

What does it mean to simplify a rational expression?

Back

To reduce the expression to its simplest form by canceling common factors.

Front

What is the factored form of x² - 16?

Back

(x + 4)(x - 4) (Difference of squares)

Front

What are the possible pairs of integers that multiply to 32?

Back

(1, 32), (2, 16), (4, 8), (-1, -32), (-2, -16), (-4, -8)

Front

How do you find the perimeter of a rectangle with sides 3x and 4x?

Back

Perimeter = 2(3x + 4x) = 14x

Front

What is the area of a rectangle with length 5x and width 2x?

Back

Area = 5x × 2x = 10x²

Front

What is the simplified form of (x + 6)/(x - 5)?

Back

(x + 6)/(x - 5) (Already in simplest form)

Front

What is the definition of a rational expression?

Back

A ratio of two polynomials.

Front

What does it mean to factor a polynomial?

Back

To express it as a product of its factors.