this is how to figure out if you can factor a simple trinomial or if it even is a simple trinomial

first you look if the the terms have a greatest common factor (GCF). No? that’s ok, now check if you have a difference of squares, remember to have a difference of squares you must have two terms, perfect squares, and it must be a subtraction. If you don’t have a difference of squares that’s still ok, time to check if you got a pattern. In this case we do so we can factor. Check if it is a simple trinomial or if it’s an ugly trinomial, it’s easy to tell because if there is a lead coefficient more than 1 it’s an ugly trinomial and you have to do more work than we do now. Now you just look for what would work with FOIL and that is how you factor

like my last post this is a method of multiplying but not just binomials I just used binomials to example this expression

this is an easier way to multiply binomials because you can really see it here where the 6x and the 5x add together, it’s basically like a multiplication table where you just fill in the boxes and do the equation

This method of multiplying binomials is called the claw or FOIL which stands for front, inside, outside, and last

It’s one of the more simpler ways to multiply binomials and what you do is take the first two numbers or variables in this case and you multiply and with this question it equals X squared than we take it to the outside and inside which are most likely going to be like terms and with this question it was, it was 6x and 5x and since they’re both positive they equal 11x, to simplify that you basically just add them when it’s all positive and then finally you multiply the final two to give you 30

This here are the three equations possible with sine, cosine, and tangent as well as the three places you could have a variable and you need to find out what the variable is.

for the first equation you have a tangent equation and they’ve already given you the opposite and adjacent and now you have to find out what the variable equals so you have to turn to inverse tangent and divide the opposite over adjacent then multiply inverse tangent with the division you just did. For the cosine equation you have the reference angle and the hypotenuse and they’re asking you to find the adjacent side so what you do is take the reference angle and multiply it with cosine then multiply that with the hypotenuse which should give you the adjacent side. for the third you have a sine equations and they’ve given you the reference angle and the opposite side and the variable is in place of the hypotenuse so what they want you to do is take the opposite side and divide it with sine times 23 which should give you the hypotenuse and you have to always make sure your results make sense and to not concentrate on your illustration of the triangle but only on the information given to you

calculating a sphere versus a hemi-sphere is basically taking a sphere and cutting the calculations in half

for volume you literally take the calculations as you can see from 4/3 there and you cut it in half and you have 4/6 for the hemi-sphere. For surface area it’s not exactly half you just take one off the 4