Question

If x3 -5x2 - px +24 = (x-4).q(x), then what is the value of p?

Answer 1

Answer

Step-by-step explanation:

remainder theorem:

dividend =divisors X quotient + remainder

therefore, let f (X)=x^3 +(kx +8)x + k

                            =x^3 + kx x^2+8x+k

Dividing if(X) by x+1 gives remainder as R 1

therefore f(-1)=R 1

also ,f(2) =R 2

therefore f(-1)=(-1)^3+k(_1) ^2+8(-1)+ k

                      =-1 +k-8+k

                      =2k-9= R 1

f(2)=(2)^3 + k(2) ^3 +8 X 2 + k

    =8+4K+ 16 +K

     =5k + 24 =R 2

also, sum  of remainders=R1+R1=1

therefore,(2k-9)+(5k+ 24) = 1

                7 k+ 15 =1

               7k=-14

                k =-2

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