Therefore:

Begin by factoring out a 2:

Then, we recognize that the trinomial can be factored into two terms, each beginning with :

Since the last term is negative, the signs of the two terms are going to be opposite (i.e. one positive and one negative):

Finally, we need two numbers whose product is negative thirty-five and whose sum is positive two. The numbers and fit this description. So, the factored trinomial is:

Multiply both sides by 3:

Distribute:

Subtract from both sides:

Add the terms together, and subtract from both sides:

Divide both sides by :

Simplify:

You can factor this trinomial by breaking it up into two binomials that lead with :

You will fill in the binomials by finding two factors of 36 that add up to 5. This is achieved with positive 9 and negative 4:

You can then set each of the two binomials equal to 0 and solve for :

For quadratic equations, you need to factor in order to solve for your variable. You do this after the equation is set equal to zero. Luckily, this is already done for you! Thus, start by factoring:

into

Then, you set each factor equal to . Solve each "small" equation:

or

or

BOTH of these are answers to the equation.

Start by factoring the equation.

We will need two numbers that multiply up to and add up to . These two numbers are .

Thus, we can factor the equation.

Solving the equation will give the following solutions:

and

Since the question states that must be a positive integer, can only equal to .

Looking at , we notice that it is a perfect square trinomial.

*A perfect square trinomial is given by the form (where "a" represents a variable term and "b" represents a constant term).

*Comparing this to our trinomial, we find...

*So, we confirm it is, indeed, a perfect square trinomial.

We have one solution:

The area of a right triangle with legs of length and is

.

Substitute and for and and 600 for , then solve for :

We can now factor the quadratic expression:

Set each linear binomial to 0 and solve to get possible solutions:

Since must be positive, we throw out the negative solution.

.

This is a factoring problem so we need to get all of the variables on one side and set the equation equal to zero. To do this we subtract from both sides to get

Think of the equation in this format to help with the following explanation.

We must then factor to find the solutions for . To do this we must make a factor tree of which is 28 in this case to find the possible solutions. The possible numbers are , , .

Since is positive we know that our factoring will produce two positive numbers.

We then use addition with the factoring tree to find the numbers that add together to equal . So , , and

Success! 14 plus 2 equals . We then plug our numbers into the factored form of

We know that anything multiplied by 0 is equal to 0 so we plug in the numbers for which make each equation equal to 0 so in this case .

For quadratic equations, you need to factor in order to solve for your variable. You do this after the equation is set equal to zero. Thus, you get:

Next do your factoring:

into

Then, you set each factor equal to . Solve each "small" equation:

or or

BOTH of these are answers to the equation.