This week in pre calc 11 we learned how to solve equations using factoring. In the example 3x squared + 15x + 18 we start by checking for common factors. In this case we have a common factor of 3 making our question 3(x squared + 5x + 6)

Now that we have taken out the common factor we are left with an easier equation to solve. Next we look at 6 and find 2 numbers that multiply to it and add or subtract to 5x. There are two sets of  that multiply to 6 and add or subtract to 5, 2 • 3 and 6 •1

Since we have two possible answers the best thing to do is try both of them to see which one is correct. We start by taking our x squared + 2 + 3 + 6 and putting it into a box.

Now that we have a box we find common factors vertically and horizontally to find our equation

we see that we are left with (x + 2) (x + 3) as our answer. Now we need to foil it to verify our answer.

We have verified by foiling our answer and we got our original question which means our answer is right. One thing to remember is that if you take out a common factor at the beginning you have to show it in your answer so our final answer is 3(x + 2) (x + 3)

One thing I learned in math this week is how to divide radical expressions. The expression is either a monomial or binomial over another monomial or binomial

The reason we have to solve this is because we can’t have roots in the denominator. The way we solve this equation is by multiplying the numerator and denominator by the denominator but we have to conjugate the signs (conjugating the signs means changing it to the opposite ie. + to – or – to +).

Next we foil our two expressions:

After we foil we combine like terms:

Once we combine like terms we have our final answer

This week in math I learned about absolute value. Absolute value are two straight lines on either side of a variable. You use this when simplifying variables to ensure it’s positive when it’s an even numbered root.

One thing I learned in Math this week is how to solve questions with fractions as the exponent.

The way you solve this problem is to start with the exponent. When a fraction is an exponent you root the coefficient by the bottom number in the fraction and put the top number as the exponent.

Next you solve the root first then square it and that number is your final answer.

One thing I learned this week was how to solve mixed rational problems. An example question is 5 root3. To solve this you make the square the 5 to make it root 25 so that it is easier to solve. Next you multiply root 25 by root 3 to get root 75 which is your final answer. If you start with root 75 and were trying to solve it that way, you would do the steps in reverse.