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

[bigmike94]

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?

 

[DrClaude]

The solution presented uses 3z, so I would assume that there is a 3 missing in the last term of the first equality.

 

[bigmike94]

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

 

[bigmike94]

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

 

[DrClaude]

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 $-3 = 5x+z$.

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.

 

[bigmike94]

thank you for the help.

So can i move on with no worries about missing anything?

 

[DrClaude]

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!