Factoring algebra II..
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Factoring algebra II..

[From: ] [author: ] [Date: 11-12-31] [Hit: ]
Now that we have a >=1 we multiply a with ca*c = 4*49 = 196Now we need ax^2+ nx + dx + c so we need to find two numbers n,d that will satisfy these conditionsCondition 1: n*d = a*cCondition 2: n+d = bso we need two numbers n,d that add to 28 and multiply to 196 . Lets try 14,14(14)(14) = 196 check14+14 = 28 = b check4x^2+14x+14x+49 = 2x(2x+7)+7(2x+7)=(2x+7)(2x+7)so 4x^2+28x+196 = (2x+7)(2x+7).3).......

b). Now that we have a >=1 we multiply a with c

a*c = 4*49 = 196

Now we need ax^2+ nx + dx + c so we need to find two numbers n,d that will satisfy these conditions

Condition 1: n*d = a*c
Condition 2: n+d = b

so we need two numbers n,d that add to 28 and multiply to 196 . Lets try 14,14

(14)(14) = 196 check
14+14 = 28 = b check

4x^2+14x+14x+49 = 2x(2x+7)+7(2x+7)=(2x+7)(2x+7)

so 4x^2+28x+196 = (2x+7)(2x+7).


3).

Rule: x^3-y^3 = (x-y)(x^2+xy+y^2) for a and c
Rule: x^2-y^2 = (x-y)(x+y) for b).

a). 125x^3-8 = (5x)^3-2^3 = (5x-2)(25x^2+10x+4)
b). Factor out x: (x^2-25)(x) = (x+5)(x-5)(x)
c). x^3 - 125 = x^3-5^3 = (x-5)(x^2+5x+25)
d). I don't quite know how to solve for that, look at
http://www.wolframalpha.com/input/?i=+x^… for help
e). Factor x^3 from x^5 + 18x^4 + 81x^3 we get ----> (x^3)(x^2+18x+81)

Find a,b,c in the equation ax^2+bx+c.

x^2+ 18x + 81 ----> a = 1, b = 18, c = 81 since a = 1 we need to find two number n,d that satisfies these conditions

Condition 1: n+d = b(if there is a minus sign in front of b then include it!)
Condition 2: n*d = c(if there is a minus sign in front of c then include it!)

so we need two number that needs to multiply to 81 and add to 18. Lets try 9=n,9=d

Lets check if it satisfies the conditions

9+9 = 18 = b check
9*9 = 81 = c check

now we got the numbers n and d we start step 2

Step 2: ax^2+bx+c = ax^2+nx+dx+c

x^2+18x+81 = x^2+9x+9x+81

Step 3: we factor out things

x(x+9)+9(x+9) = (x+9)(x+9).

So x^5 + 18x^4 + 81x^3 = (x^3)(x^2+18x+81) = x^3(x+9)(x+9)

I am sorry for length and i hope this a good explanation!

Hope it helps Enjoy!

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Sum of cubes is factored as follows: a^3 + b^3 = (a + b)(a^2 - ab + b^2)
Difference of cubes: a^3 - b^3 = (a - b)(a^2 + ab + b^2)

For example: 8x^3 - y^3 = (2x)^3 - y^3 = (2x - y)((2x)^2 + (2x)y + y^2)

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For any difference of squares equation in standard form a^2 - b^2, the factored form is (a+b)(a-b)

Example: x^2 - 16 = x^2 - 4^2 (a = x and b = 4)
so x^2 - 16 = (x+4)(x-4)

Personally I would love to help you on everything else, but its Christmas Break here, and most of that math has left my memory banks. Sorry!
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