can't for the life of me undestand this

there is no example in the book; if there is i have no idea where it is. the teacher likes to use future material in tests for no reason.

These are the answers I got:

9. A
10. B
11. A
12. D

If you want me to show you how I solved them just ask.

tahts exactly what i want; a detailed walkthrough of each problem. if i can see how it is solved, it makes it much easier to do in the future.

Question 9:

Factor X^2 out of the equation:
X^2(X^2=36)
That X^2 is now equal to zero. You take the square root of both sides which gives you + and - zero because a negative squared comes out as the same as a positive squared. However in this case there is no such thing as positive or negative zero, there is just zero twice. So zero is a root twice, or a double root.

Next you have the X^2=36. Again take the square root of each side and you get + and - 6. So 6 and -6 are roots as well. Altogether you have 0 twice, 6, -6 as your answers. Which means A is your answer.

Question 10:

Multiply the factors (X-3)(X+3) together to get X^2-9=40.
Add nine to each side to balance it out to X^2=49. Take the square root of each to get your + and - 7.
Your answer is B.

Question 11:

Multiply the factors (X+2)(X+2) together (because its squared or in other words multiplied by itself once) to get (X^2+4X+4)+(7(X+2))=18.

Then multiply that 7(X+2) out to get (7X+14). Add this to the first polynomial (or equation if you don't know what that means) to get X^2+11X+18=18.

You then subtract each side by 18 to get it all balanced which as it happens makes the whole thing equal to zero.

So now you have X^2+11X=0. Take X out like this X(X+11)=0. Now that X is simply equal to zero. Which means zero is a root (and there is only one of it).

With X+11=0 you can easily see that the last root is X= -11. So your two roots are 0 and -11. The answer is A.

Question 12:

This one is easy if you know what you are doing. You won't need to multiply them all together since it is equal to zero. What you see there with that cubed root means that written out long it looks like ((X^2)-4)((X^2)-4)((X^2)-4)=0.
Just see that when you balance each side by adding 4 you will have X^2=4 and when you take the square root of each side after that the roots are + and - 2. And then since there is two other factors exactly the same your roots will be -2,2 -2,2 and -2,2 or -2 three times or a triple root and 2 three times or a triple root.

So basically the answer is -2 (triple root) and 2 (triple root). The answer is D.

Is that helpful?