Question

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

Answer 1

The given condition is must important to solve this question

Answer 2

Answer

g(x)= 2x³ + 17x + k

       (solve)

g(x)= 50 + k

therefore remainder of p(x)=100 +2k (double of 50 +k)

kx^4 + 3x³ + 6 = 100 + 2k

k(2)^4 + 3(2)³ + 6 = 100 + 2k

           (solve)

14k = 70

so k = 70 ÷ 14

k = 5

Answer: Value of k is 5

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