The polynomial g(x)=2x²+3x²+qx-1 has the same remainder when divided by (x+2x)and (x-1). find the value of constant q

Answer 1

To find the remainder when g(x) is divided by (x + 2x), we can use synthetic division:

(x + 2x) = 3x
2x^2 + 3x^2 + qx - 1 = 5x^2 + qx - 1

Now, to find the remainder when g(x) is divided by (x - 1), we can again use synthetic division:

(x - 1) = -1
5x^2 + qx - 1
-5 5 + q -5

Since the remainder is the same for both divisions, the result for both divisions should be the same:

5 + q = -5
q = -10

Therefore, the value of the constant q is -10.