Is this a typo or am I missing something? (polynomial equations)

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In summary, the conversation discusses the issue of a missing term in a polynomial expression. The conversation also mentions a second method that does not use the missing term but still yields the same solution. The book may need to be revised due to this error. Ultimately, the issue is resolved and there are no further concerns.
  • #1
bigmike94
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TL;DR Summary
i cannot figure out where the 3z comes from
The question is asking to express a polynomial in terms of 3 other given polynomials, which in this case should be very straight forward but i am having issues, with the end terms on the second line they have grouped the constants that have a t^0. They have put 5x+3z, my answer says 5x+z, because they're the only terms with t^0 attached. Every other part of the answer matches mine apart from that one term, which ultimately changes the whole final answer. what am I missing?

1668597132994.png
 
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  • #2
The solution presented uses 3z, so I would assume that there is a 3 missing in the last term of the first equality.
 
  • #3
bigmike94 said:
TL;DR Summary: i cannot figure out where the 3z comes from

The question is asking to express a polynomial in terms of 3 other given polynomials, which in this case should be very straight forward but i am having issues, with the end terms on the second line they have grouped the constants that have a t^0. They have put 5x+3z, my answer says 5x+z, because they're the only terms with t^0 attached. Every other part of the answer matches mine apart from that one term, which ultimately changes the whole final answer. what am I missing?

View attachment 317242

i will add that they used a second method which acknowledges the fact that there is no 3z, yet it has the same solution as using 3z, very confused

1668598063678.png
 
  • #4
DrClaude said:
The solution presented uses 3z, so I would assume that there is a 3 missing in the last term of the first equality.
But where would that come from, this is the question and i cannot see anywhere where that term comes from, i have also posted their second method that doesn't use the term 3z yet has the same solution

1668598160596.png
 
  • #5
bigmike94 said:
i will add that they used a second method which acknowledges the fact that there is no 3z, yet it has the same solution as using 3z, very confused

View attachment 317243
You can check that setting ##x=-3## and ##z=4## doesn't solve ##-3 = 5x+z##.

bigmike94 said:
But where would that come from, this is the question and i cannot see anywhere where that term comes from, i have also posted their second method that doesn't use the term 3z yet has the same solution

View attachment 317244
Then the book needs to be revised.
 
  • #6
thank you for the help.

So can i move on with no worries about missing anything?
 
  • #7
bigmike94 said:
thank you for the help.

So can i move on with no worries about missing anything?
I guess so. Good for you to see that there was a problem there!
 
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1. What is a polynomial equation?

A polynomial equation is an algebraic equation that contains one or more terms with variables raised to non-negative integer powers. It is used to represent relationships between variables and is commonly used in mathematics and science.

2. How do I know if I have made a typo in a polynomial equation?

If you are unsure if you have made a typo in a polynomial equation, you can check by simplifying the equation and comparing it to the original equation. If they are not identical, then there may be a typo present.

3. What are some common mistakes when solving polynomial equations?

Some common mistakes when solving polynomial equations include forgetting to distribute negative signs, making errors when combining like terms, and incorrectly applying the rules of exponents.

4. What steps should I follow when solving a polynomial equation?

The general steps for solving a polynomial equation are to simplify the equation, isolate the variable term, use inverse operations to remove any constants, and then solve for the variable by factoring or using the quadratic formula.

5. Can a polynomial equation have more than one solution?

Yes, a polynomial equation can have multiple solutions. The number of solutions is determined by the degree of the polynomial, which is the highest exponent in the equation. For example, a quadratic equation can have up to two solutions while a cubic equation can have up to three solutions.

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