Question

on dividing x cube minus 3 X square + X + 2 by polynomial GX the quotient and remainder where x minus 2 and minus 2 X + 4 respectively find GX​

Answer 1

Step-by-step explanation:

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Answer 2

Concept Introduction: Polynomials are really interesting to solve.

Given:

We have been Given:

${x}^{3} - 3 {x}^{2} + x + 2$

Quotient is

$(x - 2)$

Remainder is

$(4 - 2x)$

To Find:

We have to Find:

$g(x)$

Solution:

According to the problem, Let the polynomial equation be

$f(x)$

Quotient be

$q(x)$

and remainder be

$r(x)$

therefore,

$f(x) = g(x) \times q(x) + r(x)$

therefore putting the equations we get

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

that gives us

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

on division

$g(x) = {x}^{2} - x + 1$

Final Answer:

$g(x) = {x}^{2} - x + 1$

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