You are told to divide a polynomial by a monomial, right? A monomial would be something like x + 3, and your polynomial could be something like x^2 + 7x + 12. The remainder theorem tells you that if you use long division to divide the polynomial by the monomial, if you have a remainder, the monomial is NOT a factor of the polynomial. You put the polynomial under the division sign and the monomial outside the division sign and do the dividing, just like you would if you had 80 under the division sign and 10 outside. When you divide the 80 by the 10, it comes out evenly with no remainder. Same thing with this: if you can divide x^2 + 7x + 12 by x + 3 and there is no remainder, then x + 3 is a factor of the polynomial. What's up on top above the division sign is the other factor. So when you multiply the x + 3 by what's on top, you get back your polyomial. It's really a very perfect and cool thing.
Answer:
72 pieces of candy
Step-by-step explanation:
As we can see, it was AFTER the 6 boys divided the candy in the bag, each boy had 3 pieces of taffy, 2 jawbreakers, and 7 lemon drops.
In order to solve this, we have to work backwards and press rewind.
First, in order to solve this, let's just keep things simple and combine all of he piece of candy that each boy received: 3 taffies + 2 jawbreakers + 7 lemon drops = 12 pieces of candy that each boy received.
Now that we know each of the 6 boys received a total of 12 pieces of candy, let's press rewind and imagine that they all put them back into the bag.
The first boy puts 12 in the original bag, then the second leaving a total of 24 now, and the third, and so on and so forth.
Once we have the 6th boy put in his share of candy back into the bag, we're left with an original count of 72 pieces of candy.
OR
You can just take the total amount of candy each boy got (12) and multiply it to the number of boys (6) to get 72 pieces of candy.
Answer:
x= -1/9
Step-by-step explanation:
6+2x=5-7x
-2x. -2x
6=5-9x
-5. -5
1=-9x/-9
-1/9=x
Take into account, that in general, a cosine function of amplitude A, period T and vertical translation b, can be written as follow:
In the given case, you have:
A = 4
T = 3π/4
b = -3
By replacing you obtain:
Hence, the answer is:
f(x) = 4cos(8/3 x) - 3
