Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:(i) p(x)=x3−3x2+5x−3, g(x)=x2−2(ii) p(x)=x4−3x2+4x+5, g(x)=x2+1−x(iii) p(x)=x4−5x+6, g(x)=2− x2

Question

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:(i) p(x)=x3−3x2+5x−3, g(x)=x2−2(ii) p(x)=x4−3x2+4x+5, g(x)=x2+1−x(iii) p(x)=x4−5x+6, g(x)=2− x2

Filo · Accepted Answer

(i)                        x−3           x2−2)x3−3x2+5x−3​                       x3               −2x                       ________________                                −3x2+7x−3                                −3x2           −6                       ________________                                              7x−9Quotient=x−3Remainder=7x−9(ii)                      x2+x−3     x2−x+1)x4−3x2+4x+5+0x3​                      x4+x2                      −x3                     ______________________                   x3+4x2+4x+5                   x3−x2+x                     ______________________                            −3x2+3x+5                            −3x2+3x−3                     ______________________                                              8Quotient=x2+x−3Remainder=8(iii)                    −x2−2            2−x2)x4+0x3+0x2−5x+6​                         x4              −2x2                         ____________________                         0x3+2x2−5x+6                                 +2x2            −4                         _____________________                                           −5x+10Quotient=−x2−2Remainder=−5x+10.

Question Text	Divide the polynomial $p (x)$ by the polynomial $g (x)$ and find the quotient and remainder in each of the following: (i) $p (x) = x^{3} - 3 x^{2} + 5 x - 3, g (x) = x^{2} - 2$ (ii) $p (x) = x^{4} - 3 x^{2} + 4 x + 5, g (x) = x^{2} + 1 - x$ (iii) $p (x) = x^{4} - 5 x + 6, g (x) = 2 - x^{2}$
Answer Type	Text solution:1
Upvotes	150

Divide the polynomial $p (x)$ by the polynomial $g (x)$ and find the quotient and remainder in each of the following:
(i) $p (x) = x^{3} - 3 x^{2} + 5 x - 3, g (x) = x^{2} - 2$
(ii) $p (x) = x^{4} - 3 x^{2} + 4 x + 5, g (x) = x^{2} + 1 - x$
(iii) $p (x) = x^{4} - 5 x + 6, g (x) = 2 - x^{2}$

Text solutionVerified

Practice questions from similar books