3x2 − 4x − 1

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3x2 − 4x − 1

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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i just need help figuring this out
factorization right?
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

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Other answers:

can you help?
can you help
  • phi
Part A: What is the total length of the two sides, 1 and 2, of the triangle? to do that , add the two sides
  • phi
to add , write down the length of 1 side, put in a "+" sign, and the write the other side
  • phi
side 1 is \( 3x^2 − 4x − 1 \) side 2 is \( 4x − x^2 + 5 \)
2x^2+4
  • phi
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
Yea
  • phi
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)
wait so part a is just 2x^2+4 ?
  • phi
in other words: perimeter - (two sides) 5x3 − 2x2 + 3x − 8 - (2x^2+4)
  • phi
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)
5x3−4x2+3x−12
  • phi
most excellent. the tricky part with subtraction is to remember the minus applies to all of the terms in (2x^2+4)
So, is that part B?
  • phi
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
  • phi
your answer for B is good
i dont understand part C
  • phi
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.
so your saying it will have 2 or more terms?
  • phi
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.
do x^2 + x - (x^2+x) =0 and that will be the answer?
for part c
  • phi
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.
yea
  • phi
showing that polynomials are closed under subtraction/addition
okay

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