divide x3+4x2-3x-10 by x+1 and verify your remainder by remainder theorem - Maths - Polynomials

Question

divide x3+4x2-3x-10 by x+1 and verify your
remainder by remainder theorem

Varun.Rawat · Accepted Answer

x + 1 ) x3  +  4x2  -  3x  -  10( x2 + 3x - 6             x3   +  x2             0    + 3x2   -  3x                    + 3x2   +  3x                         0       - 6x  -  10                                  - 6x   -   6                                       0     -  4So, quotient = x2 + 3x - 6remainder = -4VERIFICATION BY REMAINDER THEOREM :Let px = x3  +  4x2  -  3x  -  10Let gx = x + 1Now, zero of gx is given by solving the equation,      gx = 0⇒x + 1 = 0⇒x = -1By remainder theorem, when px is divided by gx, then required remainder isp-1
Now,p-1 = -13 + 4-12 - 3-1 - 10           = -1 + 4 × 1 + 3 -10           = -1 + 4 + 3 -10 = 6 - 10 = -4So, remainder = p-1 = -4