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

1.	If x3 -5x2 - px +24 = (x-4).q(x), then what is the value of p?
Answer» 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 hope u have been understood mark me as brainlist thanku

Answer»

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

hope u have been understood

mark me as brainlist

thanku

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