Question

Given Q(x) = 7x − 3 and P(x) = 7x3 − 3x2 + 42x − 27, find P(x) Q(x) . (Divide using long division.)

Answer 1

Complete question:

Given Q(x) = 7x − 3 and P(x) = 7x3 − 3x2 + 42x − 27, find P(x) ÷ Q(x) . (Divide using long division.)

Answer:

`(7x^3 \ - \ 3x^2 \ + \ 42x \ - \ 27)/(7x \ - \ 3) = \ \ x^2 + 6 \ \ (-9)/(7x \ - \ 3)`

The quotient = x² + 6 and the remainder = - 9

Explanation:

Given;

Q(x) = 7x − 3

P(x) = 7x³ − 3x² + 42x − 27

To divide P(x) by Q(x) using long division, we apply the following method;

x² + 6

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7x − 3 √ 7x³ − 3x² + 42x − 27

− (7x³ - 3x²)

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42x − 27

− (42x − 18)

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− 9

`Therefore, \ (7x^3 \ - \ 3x^2 \ + \ 42x \ - \ 27)/(7x \ - \ 3) = \ \ x^2 + 6 \ \ (-9)/(7x \ - \ 3)`

The quotient = x² + 6 and the remainder = - 9