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=Question 3

=Question 4

=Question 5

 

Question 4. 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).

Question 4. 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).

According to division algorithm
Dividen= Divisor × Quotient    + Remainder
p(x)      = g(x)       × q(x)           + r(x),
plug the value in formula we get
x³ – 3x² + x + 2       = g(x) *(x-2)   - 2x + 4
Add 2x and subtract 4 both side we get

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

simplify and divide by x/2 we get

(x³ – 3x² + 3x– 2)/(x-2) = g(x)


 So we get g(x)  = x^2 – x +1



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Question 4. On dividing x3 – 3x2 + x + 2 by a polynomial g(x), the quotient and remainder

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