Question

Polynomial x3 + 5x2 + ax -7 is divided by (x-3) then remainder is 47. Find the value of 'a' ?

Answer 1

P(x)= x3 + 5x^2 + ax - 7 and g(x) = x - 3
According to the question,
=>x - 3 = 0
=>x = 3

Put the value of x in p(x)
=>(3)^3 + 5 × (3)^2 + a × (3) - 7 = 47
=>27 + 5 × (9) + 3a = 47 +7
=>27 + 45 + 3a = 54
=>72 + 3a = 54
=> 3a = 54 - 72
=> 3a = -18
=> a = -18/3
=> a = -6

SO,VALUE OF a = -6

Answer 2

SOLUTION :

let

P(x) = x³ + 5x² + ax - 7

and g(x) = (x-3) , x = 3

According to the question

When P(x) is divided by g(x) the remainder is 47

So,

P(3) = (3)³ + 5(3)³ + a(3) - 7 = 47

      = 27 + 45 + 3a - 7 = 47

      = 72 - 7 + 3a = 47

        = 65 + 3a = 47

      = 3a = 47 - 65

        = 3a = -18

        = a = -18÷3

        = a = -6

Hence

the value of 'a' is -6