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anonymous
 one year ago
3x2 − 4x − 1
anonymous
 one year ago
3x2 − 4x − 1

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i just need help figuring this out

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i 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

phi
 one year ago
Best ResponseYou've already chosen the best response.1Part A: What is the total length of the two sides, 1 and 2, of the triangle? to do that , add the two sides

phi
 one year ago
Best ResponseYou've already chosen the best response.1to add , write down the length of 1 side, put in a "+" sign, and the write the other side

phi
 one year ago
Best ResponseYou've already chosen the best response.1side 1 is \( 3x^2 − 4x − 1 \) side 2 is \( 4x − x^2 + 5 \)

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes. 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

phi
 one year ago
Best ResponseYou've already chosen the best response.1next 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)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait so part a is just 2x^2+4 ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1in other words: perimeter  (two sides) 5x3 − 2x2 + 3x − 8  (2x^2+4)

phi
 one year ago
Best ResponseYou've already chosen the best response.12x^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)

phi
 one year ago
Best ResponseYou've already chosen the best response.1most excellent. the tricky part with subtraction is to remember the minus applies to all of the terms in (2x^2+4)

phi
 one year ago
Best ResponseYou've already chosen the best response.1the 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i dont understand part C

phi
 one year ago
Best ResponseYou've already chosen the best response.1polynomials 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so your saying it will have 2 or more terms?

phi
 one year ago
Best ResponseYou've already chosen the best response.1when 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 nonpolynomial 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do x^2 + x  (x^2+x) =0 and that will be the answer?

phi
 one year ago
Best ResponseYou've already chosen the best response.1no. (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.

phi
 one year ago
Best ResponseYou've already chosen the best response.1showing that polynomials are closed under subtraction/addition
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