When - - - - - - - - - is divided by - the quotient is - and the remainder is - Find -

Step 1: Write the terms in the standard form nbsp;𝒙^4+𝒙^3−2𝒙^𝟐+𝒙+2 = (x 1)g(x) + (3) and then simplify for g(x) g(x) = (𝒙^4+𝒙^3−2𝒙^𝟐+𝒙 1)/ (x 1) Step 2: P ...

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Standard X

Mathematics

Division Algorithm for Polynomial

When 𝒙𝟒 + �...

Question

When $x^{4} + x^{3} - 2 x^{2} + x + 2$ is divided by 𝒈(𝒙), the quotient is 𝒙−𝟏 and the remainder is 𝟑. Find 𝒈(𝒙).

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Solution

Step 1: Write the terms in the standard form
$x^{4} + x^{3} - 2 x^{2} + x + 2 = (x - 1) g (x) + (3)$ and then simplify for g(x)
$g (x) = \frac{(x^{4} + x^{3} - 2 x^{2} + x - 1)}{(x - 1)}$

Step 2: Perform the division algorithm to find g(x)

divide the polynomial $x^{4} + x^{3} - 2 x^{2} + x - 1$ by $x - 1$ using the long division method.

The quotient is $x^{3} - x^{2} + 1$ and remainder $0$

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When x4+x3−2x2+x+2 is divided by 𝒈(𝒙), the quotient is 𝒙−𝟏 and the remainder is 𝟑. Find 𝒈(𝒙).

When $x^{4} + x^{3} - 2 x^{2} + x + 2$ is divided by 𝒈(𝒙), the quotient is 𝒙−𝟏 and the remainder is 𝟑. Find 𝒈(𝒙).