Question

Without actual division prove that the polynomial 2x^2+7x+3 is a factor of 23x+6x^3+25x^2+6

Answer 1

6x^3 + 25x^2 + 23x + 6 = 6x^3 + 21x^2 + 9x + 4x^2 + 14x + 6
= 3x(2x^2 + 7x + 3) + 2(2x^2 + 7x + 3)
= (2x^2 + 7x + 3)(3x + 2)

So (2x^2 + 7x + 3) is a factor