The product of the zeroes of a polynomial can be found by multiplying all the roots together. In this case, we have a polynomial given by the product of two linear factors: (3x-6) and (7x-21). To find the product of the zeroes, we need to determine the values of x that make each factor equal to zero.

Finding the zeroes of the first factor: (3x-6)
To find the zeroes of the first factor, we set (3x-6) equal to zero and solve for x:

3x - 6 = 0

Adding 6 to both sides:

3x = 6

Dividing both sides by 3:

x = 2

Therefore, the first factor has a zero at x = 2.

Finding the zeroes of the second factor: (7x-21)
Similarly, we set (7x-21) equal to zero and solve for x:

7x - 21 = 0

Adding 21 to both sides:

7x = 21

Dividing both sides by 7:

x = 3

Thus, the second factor has a zero at x = 3.

Product of the zeroes
Now that we have found the zeroes of each factor, we can find the product of the zeroes by multiplying them together:

Zeroes: x = 2 and x = 3

Product of zeroes: 2 * 3 = 6

Therefore, the product of the zeroes of the polynomial (3x-6)(7x-21) is 6.

Summary:
To find the product of the zeroes of the given polynomial (3x-6)(7x-21), we first determined the zeroes of each factor by setting them equal to zero and solving for x. The first factor (3x-6) has a zero at x = 2, and the second factor (7x-21) has a zero at x = 3. Finally, we multiplied the zeroes together to find the product, which is 6.

2×3=6