If the polynomial x(power 4)-6x(power 3)+16x(power 2)-15x+10 is divided by another polynomial x(power 2)-2x-k , the remainder comes out to be (x+a) . Find k and a ?

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1 Answer

+1 vote
answered Jun 7, 2016 by biswayan10 Basic (37 points)

PROVING BY REMAINDER THEOREM:

X4-6X3+16X2-15X+10 = (x2-2x-k)(q(x)) +(x+a)   

[any number=divisor  x  quotient + remainder]   {q(x) is a function of x which i am considering as the quotient}

X4-6X3+16X2-15X+10-x-a = (x2-2x-k)(q(x))

X4-6X3+16X2-16X+10= (x2-2x-k)(q(x))+a

When x=2,

16-48+64-32+10=(4- 4-k)(q(x))+a

-22 = -k(q(x))+a

  • a=k(q(x))-22

When x= -k,

solve it and divide the equations the q(x) will be eliminated and solve the rest coz i am still figuring this out

GOOD LUCKyes

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