Question

On dividing x³-3x²+x+2 by a polynomial g(x), the quotient and remainder were x-2 and -2x+4 respectively, then g(x) is equal to *

Answer 1

Answer:

Step-by-step explanation:

We know that, Dividend = Quotient * Divisor + Remainder

⇒f(x) = q(x)*g(x) +r(x)

⇒ x³-3x²+x+2 = (x-2)*g(x) + (4-2x)

⇒ x³-3x²+x+2-4+2x = (x-2)*g(x)

⇒ x³-3x²+3x-2 = (x-2)*g(x)

⇒ g(x) = $\frac{x^3-3x^2+3x-2}{(x-2)} = \frac{(x-2)(x^2-x+1)}{(x-2)} = x^2-x+1$

Answer 2

Step-by-step explanation:

Step-by-step explanation:

We know that, Dividend = Quotient * Divisor + Remainder

⇒f(x) = q(x)*g(x) +r(x)

⇒ x³-3x²+x+2 = (x-2)*g(x) + (4-2x)

⇒ x³-3x²+x+2-4+2x = (x-2)*g(x)

⇒ x³-3x²+3x-2 = (x-2)*g(x)

⇒ g(x) = \frac{x^3-3x^2+3x-2}{(x-2)} = \frac{(x-2)(x^2-x+1)}{(x-2)} = x^2-x+1

(x−2)

x

3

−3x

2

+3x−2

=

(x−2)

(x−2)(x

2

−x+1)

=x

2

−x+1

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