Question

the polynomial p (x)=kx^4 +3x^3+7 when divided by x-2 leave a remainder which is triple the remainder left by the polynomial g (x)=2x^3+17x+k when divided by x-1 find the value of k

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Answer 1

Answer:

Note: Remainder theorem:-

If a polynomial p(x) is divided by (x-a) then the remainder is given by;

r = p(a).

Solution:

Case(1):

When the polynomial

p(x) = kx^4 + 3x^3 + 7 is divided by

(x-2) , then the remainder is given as;

=> r1 = p(2)

=> r1 = k(2)^4 + 3(2)^3 + 7

=> r1 = 16k + 24 + 7

=> r1 = 16k + 31

Also,

g(x) = 2x^3 + 17x + k is divided by

(x-1) ,then the remainder is given as;

=> r2 = 2(1)^3 + 17(1) + k

=> r2 = 2 + 17 + k

=> r2 = k + 19

According to the question,

=> r1 = 3r2

=> 16k + 31 = 3(k + 19)

=> 16k + 31 = 3k + 57

=> 16k - 3k = 57 - 31

=> 13k = 26

=> k = 26/13

=> k = 2

Hence, the required value of k is 2.

Answer 2

Answer:

k is 2.

Step-by-step explanation:

k is 2.