Question

Is (x + 3) a factor of 2x^4 + 5x^3 - 2x^2 + 5x + 3?

Answer 1

Let f(x) = 2x^4 + 5x^3 - 2x^2 + 5x + 3

To know whether (x + 3) is a factor, substitute  x = -3 in f(x)

                                 = 2(-3)^4 + 5(-3)^3 - 2(-3)^2 + 3

                                 = 2(81) + 5(-27) - 2(9) + 3

                                 = 162 - 135 -18 + 3

                                 = 165 - 168

                                 = -3 is not equal to 0

If the obtained value is zero then only we can say that (x + 3) is a factor of f(x).

But the value is non zero. Hence ( x + 3) is not a factor for 2x^4 + 5x^3 - 2x^2 + 5x + 3.