That said, they've never seen how to factor the sum and difference of cubes. And we didn't want to just TELL them. So, instead, we thought of a way to have them figure it out!

Follow the link here for the whole handout, titled "4. Factoring"

Overall, I think it's helping students to make connections! Thought I would share the resource!

**Warm-up**

1.
Given 4 is an
x-intercept of f(x), what must be a factor of f(x)?

2.
A

*portion*of the graph of a polynomial is below, what (if anything) do you know about…a) the degree of the polynomial?

b) its end behavior?

c) its roots? Their multiplicity?

3.
Identify the
end behavior and x-intercepts of

a. h(x)=x(x+3)^3(2-x) b)g(x)=-x^5 +4x^4-4x^3

c) f(x)=x^5-3x^4-x^3+3x^2

Almost all the polynomials
we have explored so far have been in factored form, which is convenient as we
can easily find the intercepts. Sadly,
polynomials are often in standard form, which is far less convenient. We already know to take a quadratic (a second
degree polynomials) from standard from to factored form (by factoring). This worksheet will serve as a review of
those methods as we all exploring a few other ways of factoring as well.

**Sum/ Difference of Cubes**

1.
On Desmos, or
your graphing calculator, graph y = x^3 + 8

a. What is the
x-intercept? What is its multiplicity?

b. Given your answer above, what must be a factor of x^3 + 8?

This
means that (x^3 + 8)=(answer from above)(

*something)*. But how do we find that*something?**c. What degree does*

*something*have to be?

Therefore (x^3 + 8)=(answer from above)(

*ax^2 + bx +c)*.
d. Using what you
know about distribution, what does

*a*have to be?*c?**e. Find*

*b*.

f. So factored, x^3 + 8 = ( ) ( ).

2.
Try to same
process to factor, x^3 - 27

What you hopefully found
is that

(insert answer to first) and (answer to second) (check your answers)

These are categorized as
the

**sum and difference of cubes**. And are factorable as
Give formulas here!