Question

divide polynomial 3 x cube minus 2 X square + 5 x minus 5 by 3 X + 1 and verify division algorithm ​

Answer 1

Solution →

Let ,

=> f(x) = 3x³ - 2x² + 5x - 5

=> g(x) = 3x + 1

f(x) ÷ g(x) →

3x + 1) 3x³ - 2x² + 5x - 5 ( x²- x + 2

3x³ + x²

(-) (-)

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-3x² + 5x

-3x² - x

(+) (+)

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6x - 5

6x + 2

(-) (-)

__________________

- 7

=> Now ,

Reminder = -7

Quotient (Q) = x² - x + 2

We know that →

• Divisors × Quotient + Reminder = Dividend

So ,

Divisor × Quotient + Reminder

= (3x + 1) × (x² - x + 2) + (-7)

= 3x³ - 3x² + 6x + x² - x + 2 - 7

= 3x³ - 2x² + 5x -5 = Dividend

Hence , the Division algorithm is proved.

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