Question:I'm in Algebra II & I don't even know how to factor. :|| Help would be greatly appreciated! I really want to learn how to do it so any tips or anything would be great.

4. 6x^2 - 7x - 3
6. x^2 - 11x + 28
7. 2x^2 + 13x + 6
11. 3y^2 + 16y + 5
12. 6x^2 + 17x + 5
13. 2x^3 - 3x^2 + 4x - 6
14. 3y^3 - 4y^2 - 6y + 8
15. y^5 - 5y^3 - 4y^2 - 20
16. 4x^2 - 8x - 45
17. 12x^2 - 25x - 7
18. 12x^2 + 13x - 14
19. 35x^2 + 37x - 6
20. 35x^2 + 27x - 18
21. 14x^2 + 3x - 27
23. 8a^2 - 10a + 3
24. 4y^2 + 8y + 3
26. 6x^2 + 19x + 15
27. 5x^2 - 26x + 5
29. 20x^2 + 13x + 2
30. 3x^2 - 42x + 147

The Reverse of Factoring is FOILing; FOIL = First, Outside, Inside, Last. Using #4 as an example, the First terms are 3x and 2x, which when multiplied together is 6x^2. Outside refers to 3x and -3 which when multiplied together is -9x. Inside refers to 2x and 1 which when multiplied equals 2x. In the standard ax^2 + bx + c formula, the sum of the Outside and Inside gives you the 'bx' term. Thus, -9x + 2x = -7x. Finally, Last terms are -3 and 1 which when multiplied is -3. Put it all together and you get 6x^2 - 7x - 3.

To solve any factoring problem, start by figuring out the the signs ( ++,+-,--). By using the second sign, which is the - (minus) sign in front of the 3, you can figure out that the only way for a negative sign to exist in multiplication, is for a positive number to be multiplied with a negative number (+a x -b).

So First Step = (x + _)(x - _)

Next step is to figure out factorsof 3, otherwise known as the "c" value (in ax^2 + bx + c). For 3, the only factors are 3 and 1 (3x1).

So Second Step = (x + 3)(x - 1)

Next we need to take into account factors of 6, a.k.a. the "ax^2" value, which incidentally are 1, 2, 3, and 6. In addition, you need to pair the ones that actually multiply to equal 6, which are 1x6 and 2x3.

Step Three of this process includes figuring out additions/subtractions that equal the "bx" value, which in this example is 7. This is when knowing how to FOIL comes in handy. You only need to solve for the "OI" part of FOIL for this part.

To apply "OI" just fill in the factors and solve for "OI" of FOIL which would be:

(6x + 3)(1x - 1)
OI = -6x + 3x = -3x

(1x + 3)(6x - 1)
OI = -1x + 18x = 17x

(2x + 3)(3x - 1)
OI = -2x + 9x = 7x

(3x + 3)(2x - 1)
OI = -3x + 6x = 9x

In the 3rd attempt we got "7x". However, we need "-7x" so it just means to switch the signs. Thus,
(2x - 3)(3x + 1)
OI = 2x - 9x = -7x

Now that -7x matches with your "bx" value, you know that you have finally solved the problem giving you the final answer of:
(2x - 3)(3x + 1)

Ta da. The more you practive, the better you'll get and you'll be able to follow the steps in your head (like me) and before you know it, be able to solve these questions in a matter of seconds. Good luck.

4. 6x^2 - 7x - 3
=(3x+1)(2x-3)

6. x^2 - 11x + 28
= (x - 7)(x - 3)

7. 2x^2 + 13x + 6
= (2x + 1)(x + 6)

11. 3y^2 + 16y + 5
= (3y + 1)(y + 5)

12. 6x^2 + 17x + 5
= (3x + 1)(2x + 5)

13. 2x^3 - 3x^2 + 4x - 6
Sorry buddy, you're going to have to do long division for cubic factorial.on paper.

14. 3y^3 - 4y^2 - 6y + 8
Sorry buddy, you're going to have to do long division for cubic factorial.on paper.

15. y^5 - 5y^3 - 4y^2 - 20
Sorry buddy, you're going to have to do long division for cubic factorial.on paper.

16. 4x^2 - 8x - 45
= (2x - 9)(2x + 5)

17. 12x^2 - 25x - 7
= (4x + 1)(3x - 7)

18. 12x^2 + 13x - 14
= (4x + 7)(3x - 2)

19. 35x^2 + 37x - 6
= (7x - 1)(5x + 6)

20. 35x^2 + 27x - 18
= (7x - 3)(5x + 6)

21. 14x^2 + 3x - 27
= (7x - 9)(2x + 3)

23. 8a^2 - 10a + 3
= (4a - 3)(2a - 1)

24. 4y^2 + 8y + 3
= (2y + 3)(2y + 1)

26. 6x^2 + 19x + 15
= (3x + 5)(2x + 3)

27. 5x^2 - 26x + 5
= (5x + 1)(x + 5)

29. 20x^2 + 13x + 2
= (5x + 2)(4x + 1)

30. 3x^2 - 42x + 147
= (3x - 28)(x - 7)
For the first, 6x^2-7x-3
you look at it & decide what parts of the outside numbers can make the inside number: how can the factors of 6 (1,2,3,6) and 3 (1,3) make a -7? It looks like -9+2, right?
Put up the ( ): ( ) ( )
Add the numbers to make them come out right:
(6x+2)(x-1.5)
So, that makes it 6x squared
-9x on the outside
+2x on the inside =-7x
-3 (the 2 times 1.5)

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