Given Q(x) = 7x − 3 and P(x) = 7×3 − 3×2 + 42x − 27, find P(x) Q(x) . (Divide using long division.)

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Mathematics Thành Công 4 years 2021-07-24T04:32:19+00:00 2021-07-24T04:32:19+00:00 1 Answers 7 views 0

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Captcha* Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )

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diemkieu · Answer 1 · 2021-07-24T04:33:20+00:00

Complete question:

Given Q(x) = 7x − 3 and P(x) = 7×3 − 3×2 + 42x − 27, find P(x) ÷ Q(x) . (Divide using long division.)

Answer:

$\frac{7x^3 \ - \ 3x^2 \ + \ 42x \ - \ 27}{7x \ - \ 3} = \ \ x^2 + 6 \ \ \frac{-9}{7x \ - \ 3}$

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

Step-by-step 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

———————————

7x − 3 √ 7x³ − 3x² + 42x − 27

− (7x³ – 3x²)

————————————-

42x − 27

− (42x − 18)

—————————————-

− 9

$Therefore, \ \frac{7x^3 \ - \ 3x^2 \ + \ 42x \ - \ 27}{7x \ - \ 3} = \ \ x^2 + 6 \ \ \frac{-9}{7x \ - \ 3}$

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