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anonymous

  • one year ago

3x2 − 4x − 1

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  1. anonymous
    • one year ago
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    i just need help figuring this out

  2. insa
    • one year ago
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    factorization right?

  3. anonymous
    • one year ago
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    i dont know, its part of the question The lengths of two sides of a triangle are shown below: Side 1: 3x2 − 4x − 1 Side 2: 4x − x2 + 5 The perimeter of the triangle is 5x3 − 2x2 + 3x − 8. Part A: What is the total length of the two sides, 1 and 2, of the triangle? (4 points) Part B: What is the length of the third side of the triangle? (4 points) Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points) but i just need help with that part

  4. anonymous
    • one year ago
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    can you help?

  5. anonymous
    • one year ago
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    can you help

  6. anonymous
    • one year ago
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    @phi

  7. phi
    • one year ago
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    Part A: What is the total length of the two sides, 1 and 2, of the triangle? to do that , add the two sides

  8. phi
    • one year ago
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    to add , write down the length of 1 side, put in a "+" sign, and the write the other side

  9. phi
    • one year ago
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    side 1 is \( 3x^2 − 4x − 1 \) side 2 is \( 4x − x^2 + 5 \)

  10. anonymous
    • one year ago
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    2x^2+4

  11. phi
    • one year ago
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    yes. notice the "add part" is simple. you write \[ 3x^2 − 4x − 1 + 4x − x^2 + 5 \] the harder part is combining "like terms" and making it look simple

  12. anonymous
    • one year ago
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    Yea

  13. phi
    • one year ago
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    next part. perimeter is the sum of all 3 sides to find the 3rd side, it is what is left over after subtracting off the two other sides from the total length (i.e. from the perimeter)

  14. anonymous
    • one year ago
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    wait so part a is just 2x^2+4 ?

  15. phi
    • one year ago
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    in other words: perimeter - (two sides) 5x3 − 2x2 + 3x − 8 - (2x^2+4)

  16. phi
    • one year ago
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    2x^2 + 4 is the sum of the first 2 sides when we add the 3rd side we get the perimeter 2x^2+4 + (3rd side) = perimeter or "solving for (3rd side) (3rd side) = perimeter - (2x^2+4)

  17. anonymous
    • one year ago
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    5x3−4x2+3x−12

  18. phi
    • one year ago
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    most excellent. the tricky part with subtraction is to remember the minus applies to all of the terms in (2x^2+4)

  19. anonymous
    • one year ago
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    So, is that part B?

  20. phi
    • one year ago
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    the last part, just say if you start with polynomials and add or subtract them, the answer is a polynomial... so polynomials are closed under addition and subtraction

  21. phi
    • one year ago
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    your answer for B is good

  22. anonymous
    • one year ago
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    i dont understand part C

  23. phi
    • one year ago
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    polynomials are closed under addition and subtraction means: if you add two (or subtract) two polynomials, the answer will be a polynomial sometimes operations are closed... sometimes not. for example. integers are closed under add/subtract integer + integer will always give an integer answer. on the other hand, integers are not closed under division example 4 / 2 is 2 so that is ok, but we could also do 2/4 = 1/2 and that is not an integer. so not closed.

  24. anonymous
    • one year ago
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    so your saying it will have 2 or more terms?

  25. anonymous
    • one year ago
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    @phi

  26. phi
    • one year ago
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    when we talk about polynomials we have to allow for 0 ,1 or more terms (which contradicts the "poly" (Greek for many) definition ), but people want polynomials closed under subtraction, and if we did not allow 0 then x^2 + x - (x^2+x) =0 would have two polynomials giving a non-polynomial answer. Solution: let 0 be part of the polynomials. any way, the answer to part C is, both adding and subtracting polynomials gave a polynomial as an answer.

  27. anonymous
    • one year ago
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    do x^2 + x - (x^2+x) =0 and that will be the answer?

  28. anonymous
    • one year ago
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    for part c

  29. phi
    • one year ago
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    no. (that was an extra example) for part C, say that the answers to part A (adding) and part B (subtracting) both started with polynomials, and had a polynomial as an answer.

  30. anonymous
    • one year ago
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    yea

  31. phi
    • one year ago
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    showing that polynomials are closed under subtraction/addition

  32. anonymous
    • one year ago
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    okay

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