Algebra tiles of x to the power of 4 +8x squared +12?

Answer 1

huh, what is the question??
taking a WILD guess, you are asking something about the expression:

x^4 + 8x^2 + 12
(or at least that is the common way to write what I think you said) but what you are asking about it, remains a mystery ...

if you want to factorize it, then it can be written
(x^2 + 6)(x^2 + 2)

Answer 2

I won't do your homework for you but I'll give hints.

First we need to identify what kind of polynomial this is. The largest exponent is 4th power, and the second largest in 2nd power, and the smallest is zero power. When you see this pattern, where all the powers are multiples of some whole number n, that should tell you that you need to substitute y in place of x^n. In this case, all the powers are multiples of 2 so we need to substitute y=x^2

So x^4+8x^2+12
which is (x^2)^2+8x^2+12
becomes y^2+8y+12

and now we have an ordinary quadratic.

You said you wanted to solve it using algebra tiles, so make a grid with 4 boxes, put y^2 in the lower left box and 12 in the upper right box. Now we need two numbers which when multiplied give you 12 and when added give you 8. What two numbers do that? Put those numbers in the upper left box and the lower right box, with "y" after them.

Now look at the top boxes and see what they have in common. Write their common factor to the left of the top row. Look at the bottom two boxes and see what they have in common, write that common factor to the left of the bottom row. Look at the left column, write the common factor below it. Look at the right column, write the common factor below it.

The labels you've written outside the grid tell you the two factors (y+__)(y+__). The last step is to substitute back x^2 in place of y.

Answer 3

x times x times x times x + 8x+12=24x??

Answer 4

x^4 +8x^2 + 12

Take x^2 = y

y^2 + 8y + 12 = 0
(y + 6)(y + 2) = 0

y = -6 or -2

x^2 = -6 or -2
x = i*sqrt(6) or i*sqrt(2)
x = 2.44948974 i or 1.41421356 i

Hope this helps!

Answer 5

let z=x^2
Then we have z^2+8z+12, or (z+6)(z+2)
To factor, we have z=-6 and z=-2
But since z=x^2, x^2=-6 and x^2=-2
Then x= +i*sqrt(6), +i*sqrt(2) and the
-i*sqrt(6), -i*sqrt(2)