When f(x) = 15x3 – 14x2 – 4x + 10 is divided by (3x + 2), then the remainder is:

To find the remainder of the function f(x) = 15x^3 – 14x^2 – 4x + 10 when divided by (3x + 2), we can use the Remainder Theorem.

The Remainder Theorem states that if a polynomial f(x) is divided by (x - a), the remainder is f(a).

In this case, we are dividing by (3x + 2), so we need to find the value of x that makes (3x + 2) equal to zero.

Solving the equation 3x + 2 = 0, we get x = -2/3.

Now, we substitute x = -2/3 into the function f(x):

f(-2/3) = 15(-2/3)^3 – 14(-2/3)^2 – 4(-2/3) + 10

= 15(-8/27) - 14(4/9) + 8/3 + 10

= -40/9 - 56/9 + 8/3 + 10

= -96/9 + 8/3 + 10

= -32/3 + 8/3 + 10

= -24/3 + 10

= -8 + 10

= 2

So, the remainder when f(x) = 15x^3 – 14x^2 – 4x + 10 is divided by (3x + 2) is 2.