Question

x^3-3x+3x-2 divided by x-2 using long division method​

Answer 1

Correct Question:

Using long division method, find : x³ - 3x² + 3x - 2 divided by (x - 2)

Answer:

● $\large\fbox{\sf Quotient = x^2 - x + 1}$

● $\large\fbox{\sf Remainder = 0}$

Verification:

p(x) = x³ - 3x² + 3x - 2

g(x) = x² - x + 1

★ Dividend = Quotient × Divisor + Remainder

= x³ - 3x² + 3x - 2 = (x - 2) (x² - x + 1) + 0

= x³ - 3x² + 3x - 2 = x(x² - x + 1) - 2(x² - x + 1) + 0

= x³ - 3x² + 3x - 2 = x³ - x² + x - 2x² + 2x - 2 + 0

= x³ - 3x² + 3x - 2 = x³ - 3x² + 3x - 2

Hence, Verified.

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Answer 2

${ \huge{ \bf{ \underline{question}}}}$

Solve the given question:

$\sf{ {x}^{3} - 3{x}^{2} + 3x - 2 \div x - 2}$

${ \huge{ \bf{ \underline{answer}}}}$

(in the attachment)

Steps followed :

1. Firstly , we have tried to find a number that when multiplied by (x) gives {x}^{3} . The value that satisfies the given statement is {x}^{2} hence we have taken the same .
2. Then , We have to multiply {x}^{2} by (-2) as it is a part of the divisor.
3. When we put up the values and try to subtract , we are left with {-x}^{2} + {3x} -2
4. So , now what number which when multiplied by (x-2) gives us {x}^{2} ?
5. The number that satisfies the above given statement is (-x) . Now we will multiply it by (-2)
6. When subtracted we get (x-2) and the number which when multiplied by (x-2) to get (x-2) is 1.
7. Putting up the values and subtracting we are left with remainder 0.