Question

Answer all please!

3. Explain the grouping method of factoring. Describe a scenario when the grouping method would be preferred over other methods and provide an example of this type of problem.



4. Graph one of your 2nd degree functions from question 1. Identify which function you used and the key features of your graph. Explain how to find them algebraically.



5. Using your graph from question 4, describe if the average rate of change is increasing or decreasing, from left to right. Justify your observations with calculations.

Answer 1

I can only answer #3 since the others require something from question 1, which is not shown.

The grouping method is used only when there is an even number of terms. When certain sides of the expression have a similar "coefficient", it is used. It's a little difficult to explain, but:

\[2x ^{3} + 4x ^{2} + 2x + 4\]
\[2x ^{2} (x + 2) + 2(x+2)\]
\[(2x ^{2} + 2)(x+2)\]

Answer 2

Here is question 1 and my answers, @magix430
1. Your friend runs up to you, scared that he is not ready for the upcoming quadratics test. To help him study, you will create four different quadratic functions. Then demonstrate to him how to rewrite each function as a group of factors, if possible.
The function f(x) is a difference of squares. y = x^3 -8
The function g(x) is a sum of squares. y = x^3(8)
The function h(x) is a perfect square trinomial. y = x^3 6x 8
The function j(x) can only have a GCF factored out of it. y = x^3 2x

1. y = (x 3)(x-3)
2. prime for real numbers
3. y = (x 3)^2
4. y = x(x 2)

Answer 3

Sorry, I don't remember the majority of this material - I've been out of math for 2 years now, but have been just running around trying to get what I could understand out of it. As far as I can see though, f(x) should be a 9 instead of an 8.
Sum of squares I'm not sure if it means that way, but rather more of something directed towards
\[a ^{2} + b ^{2}\]
or something.
h(x) is okay, but you might want to recheck your factorization of the final one.

Answer 4

can you help at all with #'s 4 and 5?

Answer 5

@magix430