## FANDOM

9 Pages

Problems and tutorials from Unit 1

## Basic Factoring Edit

• Simplification
• Take out GCF
• Completing the square
• Sum/Difference of Perfect Cubes*
• Remember SOAP (Same, Opposite, Always Positive)
• Sum: (a + b)(a² - ab + b²)
• Difference: (a - b)(a² + ab + b²)
• Grouping

## Heart Problems Edit

• Identify the heart piece (the one with a difference variable than the other pieces)

ex: x² + 4x + 4 - 9y²

• The "Heart Piece" is -9y² because it is the only y.
• The piece alone factors into -3y and 3y. You add these numbers into the factors of the polynomial (in this case, it's x² + 4x + 4) which factors to (x-2)(x-2)
• Final solution is (x - 2 + 3y)(x - 2 - 3y)

Sample problem

## Factoring with Fraction Exponents Edit

• Take out a GCF -- Take out whichever exponent is smaller. Then, factor.
• Remember that an exponent times an exponent is you add the exponents together. Don't multiply them!
• If you are left with a negative exponent, you have to simplify.
• Just switch the piece with a negative exponent from the numerator to the denominator, and switch the sign of the exponent (ex. -1/4 would become 1/4)

Sample problem

## Complex Fractions Edit

• Turn every piece in the numerator and denominator into a fraction.
• Make all fractions have a common demonimator through multiplication. Make sure you multiply the numerator by whatever you are multiplying the denominator in order to get the common.
• Once your common denom, take the denominators away completely.
• Simplify and factor further if necessary.
• Be careful with ones that have x and h as variables.

## Restricting Domain Edit

• Check all fractions used in the problem, during all stages of your work, and figure out which values of x or h (or another variable) make the denominator 0.
• Look at the previous problem for example
• If there is a piece under a radical, than the variable must be equal to or greater than 0 (can't have a negative under a root)
• Write points as coordinates. Use [] if including a value, () if not including a value.

Sample problem