Question

(x-2)^(2) - 9
the answer is (x+1)(x-5). why is it 5? i dont understand.

Answer 1

If you expand this,\[(x-2)^2\]you will get a polynomial of second degree. Can you do that and show me the result?

Answer 2

no. im sorry, but I dont understand any of it.

Answer 3

Ok, don't worry. I will help you. Now, to expand this we use this formula,\[(a+b)^2=a^2+2ab+b^2\]The idea is that a and b can be anything from numbers to variables. Now, we know that in your case a=x and b=(-2). So let's input them in the equation and solve it.\[(x+(-2))^2=x^2+2*x*(-2)+(-2)^2\]The result is\[(x+(-2))^2=x^2-4x+4\]Do you understand up to here?

Answer 4

\[(x -2)^{2}-9\], what is asked... to factor or find the value of x...?

Answer 5

you can factor \[(x−2)^{2}−9\] by using the difference of two squares

Answer 6

\[a^{2}-b ^{2}=(a+b)(a-b)\]

Answer 7

\[(x-2) ^{2}−3 ^{2}\]

Answer 8

but why is 5 in there, thats what i dont get at all. shouldnt it just be 2 and 3 in there and not 5?

Answer 9

\[(x−2)^{2}−3^{2}=(x-2+3)(x-2-3)\]

Answer 10

(x+1)(x-5)

Answer 11

thats simple enough i guess. im still a bit confused. but i think its ok.