Certainly! Let's find the x and y-intercepts for each polynomial:

1. y = x³ + x² - 12x:

To find the x-intercepts, we set y = 0 and solve for x. Factoring out an x, we get:

x(x² + x - 12) = 0

Setting each factor equal to zero, we get:

x = 0 (x-intercept)

x² + x - 12 = 0

Using the quadratic formula or factoring, we find the remaining x-intercepts to be:

x = 3 and x = -4.

To find the y-intercept, we set x = 0:

y = 0³ + 0² - 12(0) = 0

Therefore, the y-intercept is (0,0).

2. y = (x-2)(x-1)(x+3):

To find the x-intercepts, we set y = 0 and solve for x. By the zero-product property, we find three x-intercepts:

x - 2 = 0 -> x = 2

x - 1 = 0 -> x = 1

x + 3 = 0 -> x = -3

To find the y-intercept, we set x = 0:

y = (-2)(-1)(3) = 6

Therefore, the y-intercept is (0,6).

3. y = 2x^4 + 8x³ + 4x² - 8x - 6:

This polynomial doesn't factor easily, so finding the intercepts requires numerical methods, such as graphing or using a calculator.

To find the x-intercepts, we set y = 0 and solve for x. Using numerical methods, we find that there are two x-intercepts at approximately x = -2.535 and x = 0.535.

To find the y-intercept, we set x = 0:

y = 2(0)^4 + 8(0)^3 + 4(0)^2 - 8(0) - 6 = -6

Therefore, the y-intercept is (0,-6).

4. y = x^4 - 16:

To find the x-intercepts, we set y = 0 and solve for x. By factoring the difference of squares, we get:

(x² - 4)(x² + 4) = 0

Setting each factor equal to zero, we find two x-intercepts:

x = 2 and x = -2 (real intercepts)

To find the y-intercept, we set x = 0:

y = (0)^4 - 16 = -16

Therefore, the y-intercept is (0,-16).

5. y = x³ + 10x² + 9x:

To find the x-intercepts, we set y = 0 and solve for x. Factoring out an x, we get:

x(x² + 10x + 9) = 0

Setting each factor equal to zero, we find three x-intercepts:

x = 0 (x-intercept)

x² + 10x + 9 = 0

Using the quadratic formula or factoring, we find the remaining x-intercepts to be approximately x = -9.055 and x = -0.945.

To find the y-intercept, we set x = 0:

y = (0)^3 + 10(0)^2 + 9(0) = 0

Therefore, the y-intercept is (0,0).