lots of trouble with basic factoring!

G

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ok. ive been thru alg. 1 and geometry and am in alg. 2. but obviously i didnt understand factoring well enough back in the day, because i get almost anything that has a factoring part RIGHT all the way up until the final factoring. so if u could help id greatly appreciate it.

let me see. if it's something like x^2 + 10x +25, i can do that. because u take the square root of x^2, and u know the square root of 25 is 5, and u know that 5+5 is 10, which is the middle number. so the answer is (x + 5) (x + 5) i get that.

but when it comes to ones like 4y^2 - 12y + 9, i get confused. because the square root of 4y^2 is obviously 2y. and the square root of 9 is 3. but when u add 3 plus 3, u dont get the -12 thats in the middle. so what does that mean?

another example of a bad one is something like 6x^2 + 13x - 5 . (now before u think i'm trying to get homework answers or sumthing, these are some we did in class. i already know the answer to this one is (2x + 5)(3x -1) but i dont know how. how do u figure out how to split this up? (other then guess and check) cause i could sit there and guess and check all the possibilities and use FOIL to check until i find the right one, but that takes forever and eats up time on tests. so is there another process?
 
black0belt0babe7 said:
but when it comes to ones like 4y^2 - 12y + 9, i get confused. because the square root of 4y^2 is obviously 2y. and the square root of 9 is 3. but when u add 3 plus 3, u dont get the -12 thats in the middle. so what does that mean?
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This does not always work, but is worth a try; divide by 4 to isolate the y^2:
y^2 - 3y + 9/4 = 0

square root of 9/4 = 3/2; so: (y - 3/2)(y - 3/2) = 0
 
The way I normally aproach this sort of problem (4y^2-12y+9) is multiply the 4 by the 9 and get 36. Now two factors of thirty six that equal -12 when added together are -6 + -6. Now rewrite the problem as 4y^2-6y-6y+9. Now factor by grouping
(4y^2-6y)+(-6y+9). Now factor and you should get 2y(2y-3)-3(2y-3). The answer is (2y-3)^2. Now try the next one the same way.
 
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