# Applied Mathematics First class note: Factoring

## Quadratic Formula

Quadratic formulas work for factoring out all equations.

### Using the quadratic formula to factor out: Natural Numbers

3?^{2} – 5? + 2 = 0

### Using the quadratic formula to factor out: Irrational numbers

This equation has irrational numbers because

?^{2} – 7? + 2 = 0

If I plug them in a=1, b= -7, c=2 into the quadratic equation,

### Using the quadratic formula to factor out: No Solution

3?^{2} + 5? + 7

This equation has a negative number in square root.

*c*(NaOH) =

*n*(NaOH)

*V*(NaOH)

= 1.2345 mol dm^{-3}

### Using the quadratic formula to factor out: One real solution or (two equal solutions)

?^{2} – 6? + 9 = 0

Using the quadratic formula works for all equations that need to be factored out. However it is difficult and unnecessary to use the quadratic formula in some equations.

## Guess Work

Guesswork can be much simpler than using the quadratic formula when it comes to factoring. However you must first determine if the equation can be factored out using guesswork. Let’s look at the following equation.

?^{2} – 8? + 7

To know if guesswork can apply for an equation before factoring begins, The constant which is “7” must be the product and -8 must be the sum of two numbers that YOU are going to decide. if two numbers YOU choose cannot be 7 as its product and -9 as its sum, then this equation cannot be factored out using guesswork.

Another way to determine if guesswork can apply for a equation,

Now back to our equation and let’s see if we can find two numbers that will satisfy its product and sum for ?^{2} – 8? + 7

If we choose 1 and 7, the two numbers

Product: -1 x -7 = 7

Sum: -1 + (-7) = -8