This week i learned about how the box method is very useful for factoring with 4 terms to make it simpler. You use a box with four squares for each term, and find the like factors of the ones across and under/above each other, then you make those factors into a binomial. It’s also useful for finding a missing term. Another use is the terms diagonal to each other will always multiply to the same product, so thats how you know if you got the terms in the correct squares. Another rule is that if the first term is negative, then the common factor will be negative. There will always be two like terms, and it doesn’t matter which one is on which side, just that they’re in the correct 2 boxes. Factoring is the opposite of FOIL.

This week i learned about rationalizing the denominator of a radical division/fraction, which is used when theres a binomial radical denominator to make the division possible. To rationalize the denominator, you have to multiply both the numerator and denominator by the denominator’s conjugate. Multiplying by the conjugate makes the denominator a more simple number, which is easier to work with. The conjugate of a denominator will be the same as the binomial equation, except for the sign will be the opposite (+ becomes -, and vice versa). How to make the conjugate -> (√x + √y) -> (√x – √y). If the denominator is a monomial radical, you rationalize it by multiplying itself with the denominator and numerator –  7/√6 –> 7 x √6/√6 x √6. This has the same purpose as multiplying by the conjugate, to make the question simpler.

This Week I reviewed and learned new exponent laws. At first, I didn’t remember most of them, but after working with my table group and adding in all our different ideas and things we did remember, it all came back to me very easily (product law, power of a power, power of a quotient, quotient law, power of a product). The new laws (Integral exponents and rational exponents) were easy for me to understand and apply because they involved all the previous laws about exponents and roots that I’ve already learned and practiced with. Integral exponents are integer exponents, and the the negative ones, all you have to do is reciprocate by putting the power under a 1. Rational exponents are also simple, you have to make sure the exponents is a fraction, then use the base as a radicand, the denominator becomes the index, and the numerator becomes the exponent. If you were to combine these (have a power to a negative fraction), you would do the same operation as the rational exponents but with a negative numerator which becomes the exponent, or you could put the rational power under a 1, then solve from there. The key is to not have any negative exponents.