License plates are made using letters followed by digits. How many plates can be made if repetition of letters and digits is al
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Answer:
The quotient of this division is . The remainder here would be
.
Step-by-step explanation:
The numerator is a polynomial about
with degree
.
The divisor is a polynomial, also about
, but with degree
.
By the division algorithm, the quotient should be of degree , while the remainder shall be of degree
(i.e., the remainder would be a constant.) Let the quotient be
with coefficients
,
, and
.
.
Start by finding the first coefficient of the quotient.
The degree-three term on the left-hand side is . On the right-hand side, that would be
. Hence
.
Now, given that , rewrite the right-hand side:
.
Hence:
Subtract from both sides of the equation:
.
The term with a degree of two on the left-hand side has coefficient . Since the only term on the right hand side with degree two would have coefficient
,
.
Again, rewrite the right-hand side:
.
Subtract from both sides of the equation:
.
By the same logic, .
Hence the quotient would be .
