Finding the Divisor Polynomial g(x)

Given:
Polynomial: 3x³ - 4x² + 5x - 13
Quotient: 3x + 10
Remainder: 16x - 43

Step 1: Write the polynomial division problem
We have the polynomial division as follows:
3x³ - 4x² + 5x - 13 = g(x) * (3x + 10) + 16x - 43

Step 2: Express the quotient and remainder in terms of g(x)
Since the quotient is 3x + 10 and the remainder is 16x - 43, we can rewrite the division problem as:
3x³ - 4x² + 5x - 13 = g(x) * (3x + 10) + 16x - 43

Step 3: Perform polynomial division
Now, divide the polynomial using the given quotient and remainder:
3x³ - 4x² + 5x - 13 = g(x) * (3x + 10) + 16x - 43
Expanding the right side:
3x³ - 4x² + 5x - 13 = 3xg(x) + 10g(x) + 16x - 43
Rearranging the terms:
3x³ - 4x² + 5x - 13 = 3xg(x) + 10g(x) + 16x - 43
Combining like terms:
3x³ - 4x² + 5x - 13 = (3x + 10)g(x) + 16x - 43

Step 4: Compare coefficients
By comparing the coefficients of the corresponding terms on both sides of the equation, we can determine the divisor polynomial g(x):
Coefficient of x³ terms:
3 = 3, so the coefficient of x³ in g(x) is 0
Coefficient of x² terms:
-4 = 0, so the coefficient of x² in g(x) is -4
Coefficient of x terms:
5 = 10, so the coefficient of x in g(x) is 0
Constant term:
-13 = -43, so the constant term in g(x) is 30

Step 5: Write the divisor polynomial g(x)
Therefore, the divisor polynomial g(x) is:
g(x) = -4x + 30

Tell me the symbol between quotient 3x10and polynomial