Question

on dividing x3-3x2+x+2 by a polynomial g(x), the quotient and remainder were x-2 and -2x+4 respectively. find g(x)

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Question:

on dividing $\sf{ {x}^{3} - {3x}^{2} + x + 2 }$by a polynomial g(x), the quotient and remainder were x-2 and -2x+4 respectively. find g(x).

Answer:

We, Know That :-

Dividend = Divisor x Quotient + Remainder.

So, We Have

Dividend or p(x) = $\sf{ {x}^{3} - {3x}^{2} + x + 2 }$

Quotient or q(x) = x-2

Remainder or r(x) = -2x+4

To Find:

Divisor or g(x)

Now , Put The values In Given Formula By Me

That is :-

$\underline{\underline{ \fbox{ \bf{Dividend = Divisor x Quotient + Remainder}}}}$

$\longrightarrow \sf{( {x}^{3} - {3x}^{2} + x + 2 }) = g(x) \times( x - 2) + ( - 2x + 4) \\ \longrightarrow\sf{( {x}^{3} - {3x}^{2} + x + 2 }) + 2x - 4 = g(x) \times (x - 2) \\ \sf{\longrightarrow {x}^{3} - {3x}^{2} + 3x - 2 } = g(x) \times (x - 2) \\ \sf{ \longrightarrow \frac{{x}^{3} - {3x}^{2} + 3x - 2 }{x - 2} } = g(x)$

Now, Divide $\sf{{x}^{3} - {3x}^{2} + 3x - 2 }$ By (x-2)

After Dividing We Got :-

$\sf{r(x) = {x}^{2} - x + 1 }$

$\sf {\therefore \: the \: g(x) \: is \: {x}^{2} - x + 1}$

Final Answer:

$\huge \sf \red{ { {x}^{2} - x + 1}}$

To Know More :

$\sf{ \alpha + \beta = \frac{ - (b)}{a} } \\ \sf{ \alpha \beta = \frac{c \: }{a \: } }$