Question

http://prntscr.com/8v2fhv
http://prntscr.com/8v2gio

Answer 1

Let's begin with the first one, but first, some theory...
Difference of squares is a factorization identity which allows me to calculate the roots of any polynomial with the form: \(A^n - b^n\)
With ruffinis method we obtain: \((a-b)(a^{n-1}+a ^{n-2}b+...b ^{n-2}a+b ^{n-1})\).
And this last equality actually shows the pattern any exponential difference has as a factorial form, which comes in handy when conjugating square roots and so on.
So, on the problem in the forst image, on the above position, we take the expression:
\[4x^2-81=0\]
And recognize the squares, of course, \(81=9^2\) and \(4=2^2\) these are exponents you should already know about, so we will just replace them:
\[2^2x^2-9^2=0\]
But, let's associate that \(2^2x^2\) to \((2x)^2\) since "2" and "x" are multiplying each other and it respects a property of exponents. :
\[(2x)^2-9^2=0\]
And as you can see, we now can apply the difference of squares which replacing "n" for "2" on the pattern I showed to you, we get : \(a^2-b^2=(a-b)(a+b)\) and that is the formula for this factorization, where "a", in this case is represented by "2x" and "b" is represented by "9":
\[(2x-9)(2x+9)=0\]
And now, this is ready to be solved for "x", which I'll leave to you.

Answer 2

so the answer would be C

Answer 3

@Directrix

Answer 4

#1 left off here:

(2x + 9)*(2x - 9) = 0

Zero Product Property

2x + 9 = 0 or 2x - 9 = 0

2x = -9 or 2x = 9

x = ? or x = ?

Answer 5

so the answer is A?

Answer 6

No.

You have to divide each of these by 2 to solve for x.

2x = -9 or 2x = 9

Answer 7

You already answered this question earlier in the thread.

Answer 8

I got C

Answer 9

If that is #15, option C is correct if it is -9/2 and 9/2

Answer 10

For #16, click here and scroll down to see the results.

http://www.wolframalpha.com/input/?i=2x%5E2+-+11x+-+6+%3D+0

Answer 11

ok i got the answer and for the last one?

Answer 12

i got B

Answer 13

What number is the last one and what about #17?

Answer 14

B is correct for the x^2 + 5x = -1 problem.