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TASK #5

WELCOME SENATOR JESSICA CARTER

  • Are the honors standards necessary?

The algebra 2 honors standards are necessary because the play a key role in differentiating the advanced students to the average students. Without the honors standards the teachers would not be able to suit all students. As well as challenging the students who want to expand their knowledge as well as fit the advanced students.

  • Is the Honors endorsement valuable enough that scarce educational funding should be spent to subsidize it?

The honors endorsement is most definitely valuable enough that scarce educational funding should be spent to subsidize it because without the funding there would not be an honors programs of which would leave the students seeking an educational challenge unsatisfied within the learning environment.

  • How are the Honors standards from this lesson used in the real world?

The honors standards from this lesson are used in the real world specifically the workforce because they utilize the basics of mathematics especially in professions such as engineering which is the appliance of mathematics and sciences. Careers involved in physical, earth, and life sciences use complex numbers used in polynomial identities. Also the binomial theory is used in the architecture and the fundamental theorem of algebra is used in the fields based in space science such as astronomy.

TASK #4

Perform the following operations and prove closure:

2. x+4/x^2+5x+6 * x+/x^2-16

x+4/(x+2)(x+3) * x+3/(x-4)(x+4)

1/(x+2)(x-4)

1/x^2-2x-8

1. x/x+3 + x+2/x+5

2x+2/2x+8

x+1/x+4

5. Compare and contrast division of integers to division of rational expressions.

  • Divisions of integers contain one answer for each question and often involve one operation.
  • Division of rational expressions include more than one answer and involves more than one operation.
  • Division of integers is similar to the division of rational expressions because they eventually become fractions and then may or may not be simplified further.

4. x+4/x^2-5x+6 ÷ x^2-16/x+3

x+4/(x-2)(x-3) * x+3/(x-4)(x+4)

(x+4)(x^2-16)/x^2-5x+6(x+3)

x^3-16x+4x^2-64/x^3-5x^2+6x+3x^2-15x+18

x^3+4x^2-16x-64/x^3-2x^2-9x+18

3. 2/x^2-9 - 3x/x^2-5x+6

2/(x+3)(x-3) - 3x/(x-2)(x-3)

2(x^2-2x-3x+6)/x^2+3x-3x-9

2x^2-10x+12/x^2-9

Algebra 2 Honors Project

This presentation is brought you by honors algebra student Joy Kelly.

Class: Algebra 2

Teacher: Mr. Graves

TASK #2

Expand the following using the Binomial Theorem and Pascal’s triangle.

1. (x + 2)^6

X^6+12X^5+60X^4+160X^3+240X^2+192x+64

2. (x − 4)^4

X^4-16X^3+96X^2-256X+256

3. (2x + 3)^5

35x^5+240x^4+720x^3+1080x^2+810x+243

5. In the expansion of (3a + 4b)^8, which of the following are possible variable terms? Explain your reasoning. a^2b^3; a^5b^3; ab^8; b^8; a^4b^4; a^8; ab^7; a^6b^5.

TASK #3

4. (2x − 3y)^4

16x^4-96x^3+216x^2y^2-216xy^3+81y^4

TASK #1

ab^7,a^5b^3,a^4b^4,a^8,b^8; would be a possible variable term because the degrees add up to 8.

Using the Fundamental Theorem of Algebra, complete the following:

4. Draw a possible graph of the follwoing polynomial: f(x)=(x+8)^3(x+2)(x-1)^4(x-6)

Complete the following exercises by applying polynomial identities to complex numbers.

3. The following graph shows a seventh-degree polynomial:

1) Factor x2 + 64. Check your work.

(X+8) (x+8)

1. Determine how many, what type, and find the roots for f(x) = x^4 + 21x^2 − 100.

Type: 4 (degree)

How many: 2 real, 2 complex

Roots: +/-2,+/-5

2) Factor 16x2 + 49. Check your work.

(4x+7) (4x+7)

3) Find the product of (x + 9i)^2

(x+9i) (x+9i)

(x^2+18i+81i^2)

x^2+18i-81

4) Find the product of (x − 2i)^2.

(x-2i) (x-2i)

x^2-4i+4i^2

x^2-4i-4

Part 1. -5,-1,-2,4,7,-3

Part 2. (x-1), (x+3), (x-5), (x-3), (x-2), (x+7)

2. Determine how many, what type, and find the roots for f(x) = x^3 − 5x^2 − 25x + 125.

Type: 3

How many: 2 real

Roots: +/- 5

5) Find the product of (x + (3+5i))^2.

(x+3+5i)^2

(x+3+5i) (x+3+5i)

x^2+3x+5xi+3x+9+15i+5xi+15i+25i^2

x^2+10xi+6x+30i-16

Algebra 2 Honors Project

Presented by: Joy Kelly

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