[tex]x^2-4x+16+\frac{22}{x-4}[/tex]
Step-by-step explanation:
The polynomial has two terms : x³ and 42
It is divided by x-4 with has two terms : x-4
The numerator is : x³ +42 and the denominator is x-4
When dividing use long division method where:
In this case, it will be;
x-4√x³+42 -----------------divide x³ by x to get x² then multiply the denominator to get
x³-42
x³-4x² ----------perform subtraction to get
0-4x²-42--------new polynomial to be divided by x-4 to get -4x
-4x²+16x---------multiply the answer -4x by the denominator to get this
16x-42 ---------perform subtraction, the new polynomial to be divided by x-4 to get 16
16x-64-----------perform subtraction to get 22 as the remainder
The answer will be ; quotient x²-4 and the remainder is 22/x-4 which is
[tex]x^2-4x+16+\frac{22}{x-4}[/tex]
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Keywords : Polynomial function, Divisor, quotient,remainder
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