What number should he subtracted from 3x^2+5x so that the resulting polynomial leaves the remainder 1 when divided by 2x+5?

Answer 1

Then for polynomial function P(x)=3x^2 + 5x + k, for some fixed number constant k,

P(-5/2) = 1 per the remainder theorem

3(-5/2)^2 + 5(-5/2) + k = 1

3(25/4) + -25/2 + k = 1

75/4 + -25/2 + k = 1

75/5 + - 50/4 + k = 1

25/4 + k = 1

25/4 + k = 4/4

k = -21/4