Does this question have any correct answer? I can't see how any of the answer choices are correct.
1 answer:
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Use the polynomial remainder theorem. If 
is a polynomial of degree 
, then we can divide by a linear term 
to get a quotient 
and remainder 
of the form
Then when
, we get 
. In other words, the value of at tells you the value of the remainder upon dividing by .
So given that
, and the remainder upon dividing by 
is -8, we know that 
, so
Since is a polynomial (not a rational expression), then we know that divides 
exactly. In particular, the remainder term of this quotient is 0. We can use long or synthetic division to determine . I prefer typing out the work for synthetic division:
-1 | 1 -4 15 k + 8
. | -1 5 -20
- - - - - - - - - - - - - - - - - -
. | 1 -5 20 k - 12
The remainder here has to be 0, so
.
Finally, we can get the remainder upon dividing by 
by evaluating 
, which gives 
.
Then when
So given that
Since
-1 | 1 -4 15 k + 8
. | -1 5 -20
- - - - - - - - - - - - - - - - - -
. | 1 -5 20 k - 12
The remainder here has to be 0, so
Finally, we can get the remainder upon dividing
Hello from MrBillDoesMath!
Answer:
36 degrees
Discussion:
The attachment shows calculated angles in red. As a straight line has 180 degrees the missing angle at A is 180 - 72 = 108 degrees (shown in red). The missing angle at B is 180 - 144 = 36. As a triangle has 180 degrees.
x + 108 + 36 = 180 => as 180 + 36 = 144
x + 144 = 180 => subtract 144 form both sides
x = 180 - 144 = 36
Thank you,
MrB
