Question

If the polynomial 6x4+ 9 x3+ 17x2+ 23 x + 10 is divided another polynomial 2 x2+ 3 x+1 then the remainder comes out to be a x + b then find the value of a and b

Answer 1

Ans:- Given:-

p(x) = 6x⁴ + 9x³ + 17x² + 23x + 10

g(x) = 2x² + 3x + 1

r(x) = ax + b

To find value of a and b

Solution:-

Firstly divide p(x) by g(x) we get

=> (6x⁴+9x³+17x²+23x+10) ÷ (2x²+3x+1)

=> (2x²+3x+1)×(3x²+7) + (2x+ 3) ÷ (2x²+3x+1)

=> (3x²+7) + 2x + 3

now, here 2x + 3 is remainder. so,

=> ax + b = 2x + 3

=> a = 2 and b = 3

here is your answer

hope it will help you