Question

Divide the polynomial x cube minus 3 X square + 3 X + 4 by the polynomial X - 2

Answer 1

Answer:Answer:

g(x) is x² - x + 1 .

Step-by-step explanation:

Given:  dividend, p(x) = x³ - 3x² + x + 2  and quotient, q(x) = x - 2  and remainder, r(x) = -2x + 4

We have to find : Divisor, g(x)

We use Division algorithm which states that

Dividend = Quotient × Divisor + Remainder

So, we have

p(x) = q(x) × g(x) + r(x)

x³ - 3x² + x + 2 = ( x - 2 ) × g(x) + ( -2x + 4 )

( x³ - 3x² + x + 2 ) - ( -2x + 4 ) = ( x - 2 ) × g(x)

x³ - 3x² + x + 2 + 2x - 4 = ( x - 2 ) × g(x)

x³ - 3x² + 3x - 2 = ( x - 2 ) × g(x)

x³ - 3x² + 3x - 2 = ( x - 2 ) × g(x)

Now, by long division we get,

Quotient = x² - x + 1

Remainder = 0

Therefore, g(x) is x² - x

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Answer 2

HOPE THIS HELPS

Step-by-step explanation:

This is a pretty easy question and x-2 is not a factor