Factor polynomials with quadratic forms

 is an exercise under the Algebra I Math Mission. This exercise practices factoring "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using quadratic factorization methods.

Types of Problems
There are two types of problem in this exercise:
 * 1) Factor the quadratic expression as the product of two binomials: This problem has a quadratic expression and students are asked to express the product of it as standard form. Distributive property can be used to speed up this process.
 * 2) Find the length of the rectangle: This problem has several expressions on a rectangle. User is asked to determine the expression that represents the length of the rectangle and type it in the text box below.

Strategies
Knowledge of the distributive property and factoring quadratics are recommended for success on this exercise.
 * 1) In order to find the product of two polynomials, user must multiply each term in first polynomial by each term in the second polynomial. User can view this process as a double application of the distributive property.
 * 2) The expression on the left-hand side of the equation is a product of two binomials. User can replace the two terms with their product and obtain an equivalent equation (which means it will have the same solutions).

Real-life Applications

 * 1) Polynomials can be used via power series to represent many complicated functions and calculus is simpler to perform on polynomials than other functions. Thus any comfort with polynomials should increase calculus ability.
 * 2) Factoring polynomials is an important skill in solving inequalities and equations with polynomials.
 * 3) Factoring polynomials can be used for solving equations with polynomials, such as those that appear in many business models.