Factoring perfect squares

The  exercise appears under the Algebra I Math Mission. This exercise practices factoring quadratic expressions of the general perfect square forms.

Types of Problems
There are three types of problems in this exercise:
 * 1. Which binomial factor do they share?: This problem has two quadratic expressions and both of them share a common binomial factor. User is asked to find which common binomial they share.


 * 2. What is the value of __ and __ ?: This problem explains that the quadratic expression __ is a perfect square, and it can also be be factored as $$(x+d)^2$$, and both __ and __ are rational numbers. User is asked to find the value of __, and also __.


 * 3. Factor the polynomial expression completely.: This problem shows a polynomial expression and user is asked to completely factor it.

Strategies
Knowledge of perfect squares, factoring, and quadratics are essential to have success while doing this exercise.
 * 1. User can recognize perfect square terms by asking the question: "Is this term the product of a term and itself?" Perfect square terms have two characteristics:
 * 1. The coefficient of the term is a perfect square integer.
 * 2. The variables in the term are raised to even powers. This is because the square $$(x^a)^2 = x^{2a}$$ and $$2a$$ is always even for any integer $$a$$.

Real-life Applications

 * 1. Polynomials can be used in fields ranging from construction to meteorology.
 * 2. Engineers use polynomials to graph the curves of roller coasters.