Question

On dividing 2x³-5x²+1 by g(x), if remainder is 17x-6 and quotient is 2x-7 , find g(x)​

Answer 1

Ans:- Given:-

p(x) = 2x³-5x²+1

q(x) = 2x - 7

r(x) = 17x - 41

To find,

g(x) = ????

Solution:-

we know that,

=> Dividend = Divisor × quotient + remainder

=> 2x³-5x²+1 = g(x) × (2x - 7) + (17x - 41)

=> 2x³-5x²+1 - 17x + 41 = g(x) × (2x - 7)

=> 2x³-5x²-17x+41 = g(x) × (2x - 7)

=> g(x) = (2x³-5x²-17x+42) ÷ (2x-7)

=> g(x) = (x²+x-5)

here is your answer

hope it will help you