I'm studying for Intermediate Algebra - why am I so confused by the powers?

whats up HOMIIEEEEE?!?!

Anyway... I totalllyyyyy forget what factoring by grouping is lol Ans that's not good because I'm a math major. HOWEVER.!.!.!.... for this example problem you have so kindlyyyy supplied for me, I should tell you that the FIRST thing you should see is that you can factor a 5x (this is the greatest common factor of this trinomial btw) out of this trinomial.... Which will leave you with something that looks like this:

(5x) (3x^4 + 5x^2 + 2)<--------THAT 2 IS A 4 MY BAD!!!! Hahah. So you got it 👍

If this dosent help you then please elaborate on the factoring by grouping thing... Lol and I'm sure I can help.

Powers are those superscripts. It's a way of maximizing multiplication. Let us work our way up, okay. Multiplication is simply an expansion of addition, and division is an expansion of subtraction.

2(3) = 2 + 2 + 2 ... or 3 + 2 = 6

3(4) = 3 + 3 + 3 + 3 ... or 4 + 4 + 4 = 12

However, what if we took multiplication up a notch:

2^(3) = 2 * 2 * 2 = 8.

That is, we multiply 2 three times.

I will change the power, just so you get the picture:

3^2 = 3 * 3 = 9. That is, multiply 3 twice

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What does x^3 mean, it meas to multiply x by itself three times. That's great, but what is x?

5 * x^3 = 320

(5 * x^3) / 5 = 320 / 5

x^3 = 64

Now divide 64 into it's multiples to understand the cubic root, so the numbers 1 - 9.

64 / 2 = 32 ; 32 / 2 = 16 ; 16 / 2 = 8 ; 8 / 2 = 4 ; 4 / 2 = 2

So the expression makes sense:

x^3 = (2 * 2 * 2) * (2 * 2 * 2)

It's cubic so I used parentheses to grouped the 2's into sets of 3's.

If we consider each group of the same number as one number and we multiply the sets, we get:

x = 2 * 2 = 4

Sure enough ... x^3 = 64 is the same as 4^3 = 4 * 4 * 4 = 64

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But that was a waste of your time, you should have just taken the cubic root:

(x^3)^(1 / 3) = 64^(1 / 3)

x^(3 * 1 / 3) = 4

x^1 = 4

x = 4

How about another:

√(x + 4) = 16

Cancel the square root operation to both sides:

[√(x + 4)]^2 = (16)^2

x + 4 = 256

Subtract 4 to both sides:

x + 4 - 4 = 256 - 4

x = 252

Also,

x^2 = 9

√x^2 = √9

x = ± 3

Thus, x = 3, and x = -3

This is because 3 * 3 = 9, and - 3 * -3 = 9

It wouldn't work for the cubic example that I used earlier because only ...

positive * positive * positive = positive

You have to use the lowest power of x in your GCF. There is an x (to the 1) so we use that. The GCF is 5x ☜