Expert: Scott A Wilson - 6/21/2010

Question
I have absolutley no clue as to what I'm doing. I have to do step by step factoring for the polynomials below. I think I have the asnwers for them but I don't know how to do step by step factoring. I will provide the answers I have got so far, feel free to correct them if they are wrong.

1. 9-x^2
Answer : -x^2+9 (not sure of this one)

2. 4x^2+81-36x
Answer : 2(x-9)^2

3. 4y^2+16y+16
Answer: 4(y^2+4y+4)

4. x^2-25/X+5
Answer: x^3 + 5x -25 /x (all over x)

Answer
A common polynomial is a² - b².  This is the same as (a-b)(a+b) since that is
a²+ab-ab-b², and the ab's in the middle cancel, giving a²-b².

1. Note the a=3 and b=x since 3²=9.
The corrcet factors are then (3-x)(3+x).

2. Yes.

3. Yes, but more, for y² + 4y + 4 = (y+2)².
This makes the final answer 4(y+2)².

4. Note that again, the top is a²-b² where a=x and b=5.
Thus, the top factors into (x-5)(x+5).
Since this is divided y x+5, the answer is only x-5.

This is teaching that a²-b² = (a-b)(a+b).

If you're really into factoring, a³-b³ = (a-b)(a²+ab+b²) and a³+b³ = (a+b)(a²-ab+b²).
Note that the (a±b) has the same sign as the one between the cubes.
The ab in the next expression has the opposite sign as that.