Consider the polynomial function P(x)=x³+42. Divide P by x− 4, and rewrite P in the form (divisor)(quotient)+remainder.

You divide the first term of the numerator with the first term of the denominator and put that in the answer, then multiply the denominator by that answer and put the value below the numerator followed by subtraction to create a new polynomial.Repeat the steps using the new polynomial

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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