Question

Factor.

x2−6x+9

(x+9)2

(x−9)2

(x+3)2

(x−3)2

Answer 1

Please do not give Direct Answers. Explain how you got there.

Answer 2

dnt worry i didnt even see it

Answer 3

@Creativeone24 Do you know how to factor?

Answer 4

For example, can you factor: \[x^2 + x\]

Answer 5

to ,figure out the factor i think ill have to factorize the quad in the equation.

Answer 6

oh wait it doesnt have a quad i messed up

Answer 7

Let me show you some examples

Answer 8

ok

Answer 9

\[x^2 + 6x + 8\]

We need to do something called FOIL. Is this term familiar to you?

Answer 10

yes it is

Answer 11

F = First
O = Outer
I = Inner
L = Last

Say we have (a + b)(c + d)

F means you multiply the first terms of each parentheses: a times c
O means you multiply the outer term of each parentheses: a times d
I means you multiply the inner terms of each parentheses: b times c
L means you multiply the last terms of each parentheses: b times d

Answer 12

We want a setup that gives us:

\[x^2 + 6x + 8\]

\[x \times x = x^2 \]

\[(x + ?)(x + ?)\]

Whenever you see x^2, the first term of each parentheses is x.

Now. The last two terms of each parentheses is always a factor of the last term of the polynomial. This is because you get the last term of the polynomial by multiplying the last terms of each parentheses

? times ? = 8

Factors of 8: 1,2,4,8

Now, which of these terms add up to 6. We can use this approach because the outer and inner terms will just be multiply by 1x, therefore they only get a variable and the coefficient does not change.

2 + 4 = 6

\[(x + 2)(x + 4)\]

Answer 13

Lets apply this same approach to:

\[x^2−6x+9 \]

We know we start with:

\[(x + ?)(x + ?)\]

Since we have x^2

Next, what is the last term of our polynomial?

9

Factors of 9: 1,3,9

Keep in mind that this always includes positive and negative values of the factors.
So, -1, 1, -3, 3, -9, 9

So which of these factors add up to -6, and multiply to get positive 9?

Why -3 and -3.

-3 + -3 = -6

-3 times -3 = 9
neg times neg = pos

Therefore, we get

\[(x - 3)(x - 3)\]

Answer 14

Whenever you have this, it can be rewritten as:

\[(x - 3)(x - 3) = (x -3)^2\]

Answer 15

@Creativeone24

Answer 16

Grabbing lunch, I hope this helps :)

Answer 17

thnk very much it does!!!

Answer 18

@Shadow