# data[].attributes.body
How do polynomial identities apply to complex numbers?

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1.Expand (x+2)^6
x^6+12x^5+60x^4160x³+240x²+192x+64
2.Expand (x-4)^4
x^4-4x³•4+6x²4²-4x•4³-4^4
=x^4-16x³+96x²-256x-256
3.Expand (2x+3)^5
2x^5+30x^4+180x³+540x²+810x+243
4.Expand (2x-3y)^4
2x^4-24x³y+108x²y-216yx+81
5. In the expansion of (3a + 4b)^8, which of the following are possible variable terms?​
a^5b³,b^8,a^4b^4,ab^7
These variable terms are possible because their degrees add up to 8 which is the power which​ (3a+4b) was raised to.​

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Dear Senator Jessica Carter,
Being an honors student my whole life, I can gladly and proudly say that honors courses are extremely necessary for the survival of creative thinking and an outstanding work ethic of the youth of our nation. Learning through an honors curriculum engages students into thinking innovatively and applying what the learn in the classroom into the real world. Many students can benefit from the funding of honors courses as mentioned in this letter.
With respect,
Andrea Iturrino-Cotto

# data[].attributes.body
1.

(x+5)(x)+(x+2)(x+3)/(x+3)(x+5)
x²+5x+x²+5x+6/x²+8x+15
2x²+10x+6/x²+8x+15
2(x²+5x+3)/x²+8x+15
x≠-3, -5

2.
x+4/(x+3)(x+2)•x+3/(x+4)(x-4)
1/(x+2)((x-4)
x≠-2,-3, -4, 4
3.2/(x+3)(x-3)-3x/(x-2)(x-3)
2x-4-3x²+9x/(x+3)(x-3)(x-2)
-1(3x²-11x-4)/(x+3)(x-3)(x-2)
x≠-3, 3, 2
4.(x+4)/(x²-5x+6)÷(x²-16)/(x+3)
(x+4)/(x-2)(x-3)•(x+3)/(x+4)(x-4)
x+3/(x-2)(x-4)(x-3)
x≠2, 3, -3

5.Dividing integers are just dividing fractions, whereas, dividing rational expression involves dividing polynomials which have to be factored before the expressions can be simplified. Both, however, involve the method keep, change, flip.

# data[].attributes.body
1.f(x)=x^4+21x²-100
=x^4-4x²+25x²-100
=x²(x²-4)+25(x²-4)
=(x²+25)(x²-4)
(x+5i)(x-5i)(x+2)(x-2)
How many roots? 4
What type are they? 2 real & 2 complex
What are they? -5i, 5i, -2, 2

2.f(x)= x³-5x²-25x+125
How many roots? 3
What type? 3 real
What are they? 5, 5, -5

3.Part 1: Zeroes w/ possible multiplicities
(x=-5)²; (x=-1)³; (x=4)^1; (7,0)^1
Part 2: Possible factored form of the polynomial
f(x)=(x+5)²(x+1)(x-4)³(x-7)

4.f(x)= (x + 8)³(x + 6)²(x + 2)(x − 1)³(x − 3)^4(x − 6)

# data[].attributes.body
1.Expand (x+2)^6
x^6+12x^5+60x^4160x³+240x²+192x+64
2.Expand (x-4)^4
x^4-4x³•4+6x²4²-4x•4³-4^4
=x^4-16x³+96x²-256x-256
3.Expand (2x+3)^5
2x^5+30x^4+180x³+540x²+810x+243
4.Expand (2x-3y)^4
2x^4-24x³y+108x²y-216yx+81
5. In the expansion of (3a + 4b)^8, which of the following are possible variable terms?​
a^5b³,b^8,a^4b^4,ab^7
These variable terms are possible because their degrees add up to 8 which is the power which​ (3a+4b) was raised to.​

# data[].attributes.body
1.Factor: x²+64
(x+8i)(x-8i)
Check Work:
(x+8i)(x-8i)=x²+64
x²+8i-8i-64i²=x²+64
x²-64i²=x²+64
x²+64=x²+64

2.Factor: 16x²+49
(4x+7i)(4x-7i)
Check Work:
(4x+7i)(4x-7i)=16x²+49
16x²-28xi+28xi-49i²=16x²+49
16x²-49i²=16x²+49
16x²+49=16x²+49

3.Find the Product of (x+9i)²
(x+9i)(x+9i)
x²+9xi+9xi+81i²
x²+18xi-81

4.Find the Product of (x-2i)²
(x-2i)(x-2i)
x²-2xi-2xi+4i²
x²-4xi-4
5.Find the Product of (x+(3+5i))
(x+3+5i)(x+3+5i)
x²+3x+5xi+3x+9+15i+5xi+15i+25i²
x²+3x+10xi+30i-16