Question

x^3-3x^2+3x+6/x-2​ pls solve then I will follow you​

Answer 1

Question :-

• Divide (x³ - 3x² + 3x + 6) by (x - 2). ?

Solution :-

(x - 2) ) x³ - 3x² + 3x + 6 ( x² - x + 1

x³ - 2x²

(changing sign). -x² + 3x

-x² + 2x

(changing sign). x + 6

x - 2

8

So,

→ Quotient = (x² - x + 1)

→ Remainder = 8 .

_________________________

Verification :-

→ Dividend = Quotient*Divisor + Remainder.

Here,

→ Quotient = (x²-x +1)

→ Divisor = (x -2)

→ Remainder = 8

→ Dividend = x³ - 3x² + 3x + 6

Putting All values we get,

→ (x-2)(x²-x+1) + 8 = x³ - 3x² + 3x + 6

→ x³ - x² + x -2x² + 2x - 2 + 8 = x³ - 3x² + 3x + 6

→ x³ - x² - 2x² + x + 2x - 2 + 8 = x³ - 3x² + 3x + 6

→ x³ - 3x² + 3x + 6 = x³ - 3x² + 3x + 6

→ LHS = RHS . (Verified).

Answer 2

$verification:\\ \\ \implies \: dividend = divisor \times quotient + remaider \\ \\ \implies{x}^{2} - 3 {x}^{2} + 3x + 6 = (x - 2)( {x}^{2} - x + 1) + 8 \\ \\ \implies {x}^{2} - 3 {x}^{2} + 3x + 6 = {x}^{3} - {x}^{2} + x - 2 {x}^{2} + 2x - 2 + 8 \\ \\ \implies {x}^{2} - 3 {x}^{2} + 3x + 6 = {x}^{3} -3 {x}^{2} + 3x + 6 \\ hence \: verified$