algebra 1 factoring help....PLEASE!!?

Question

i'm having trouble understanding factoring problems such as:::

3x squared - 17x + 10

or

6t squared + 26t + 24


any help would be greatly appreciated!!! i have a test tomorrow!

Answer 1

(3x - 2)(x - 5)

2( 3t^2 + 13t + 12) = 2(3t + 4 )(t + 3)

You need to try factors of the first and last to see which add or subtract to give you the middle term.
Remove a common factor first if possible.

Answer 2

The answer to the first one would be (3x - 2)(x - 5) and the answer to the second one would be (3x+4)(2x+6).

One way to solve these problems is to look at the factors of the first number and of the 3rd number and see which combination works.

For example on the second problem, the factors of 6 are 6,3,2,1 and the factors of 24 are 24,12,8,6,4,3,2,1. You also know that all the numbers have to be positive since there are no minuses, or negative signs. So, you know the answer will be either (6x + a)(1x + b) or (3x + a)(2x + b). Now to find the unknowns, you know that either 6b+a=26 or 3b+2a= 26, and (a, b) has to be either (24,1), (1,24), (12, 2), (2,12), (8, 3), (3,8), (4,6) or (6, 4) (the combinations of factors that equal 24). You can just plug these pairs into the two possible equations (6x+y=26 or 3x+2y= 26) and you will find that the only solution is (6, 4) for the equations 3b+2a = 26... therefore you know the factoring is (3x+4)(2x+6).

It's kind of hard to put into words, but I hope this helps. After you do it for long enough, the solutions will come more easily. If you need some more help you can IM me on yahoo sn: sup3rgir1i. I'm a math education major so I should be able to help.

Answer 3

3x^2-17x+10 when you factoring it out you have to look for the factors of 3 and 10 and that when you add them together they will equal 17.

*** Keep in mind that two negative equal a positive, positive and a positive equal a positive and a positive and a negative equals a negative. Also when finding factors write down the factors because the first set of factors may not work. You may have to try a couple of combinations before you get the right one.

1. factors of 3x^2 are 1 and 3 (3x )(1x )

2. You have to determine what sign to use in the equation.
(3x- )(1x- )

3. Factors of 10. We can try 5 and 2. If these do not work you can try 10 and 1.

(3x-2) (1x-5)

4. To check if you have the correct answer multiply the 2 equations to get your original answer.

You will start with the outer or the first number in the equation The (3x-2)(1x-5). You will multiple the 3x (1x -5).
(3x^2-15x )

5. Next you will multiple -2 by (1x -5).
(2) (1x-5)

(3x^2 -15x-2x+10 which =

3x^2 -17x+10 your orginal problem.

6t^2+26+24

Since this the problem has a common factor you will use the greatest common factor and factor it out. the gcf is 2.

2(3t^2+13+12) = 6t^2+26+24

Now that you found the gcf you have to factor out the equation or simplify it even more.

2(3t^2+13+12)

2[(3t+4)(t+3)] To check if you have the right answer .....you multiply 3t by (t+3)

2[(3t^2+9 ) Then you will multiply 4 by (t+3).

2[(3t^2+9t+4t+12)] Your next step is to add common numbers or variables together such as the 9t +4t= 13t

2[(3t^2+13t+12)]

Next you will multiply the whole equation by 2. The gcf you factored out in the begining of the problem.

6t^2+26t+24. Which is your original problem.

I hope this information was helpful. Good look on your test.

Answer 4

3x^2 -17x + 10 the first term has a coefficient of 3, so the factors must be 3 and 1 (1x3+3)
(3x ) (x )
The possible factors of 10 are: 1 and 10, 2 and 5
using those and the 3 and 1, the middle must add up to -17. 5x3=15and 2x1 = 2. 15 + 2 = 17
they must both be negative to get -17, and -2x-5=10, the last number, so that is it.
(3x-2)(x-5) check it by FOIL. First times first,
then multiply outside, then multiply inside, then last times last. The outside and inside get added.
You have to do a lot of them, and you recognised patterns, but to begin, write down all possible factor combinations and try them one by one. Yes, it is work. It will get easier if you do some. The light will light. Here are two good sites:
http://www.coolmath.com
http://www.purplemath.com
this site will help solve any problem, EVEN personal ones:
http://en.wikipedia.org/wiki/how_to_solve_it
I spent some time, now you spend some, and you will get it, it took me a while.
Okay?

Answer 5

Doing only first problem and you try the other.
Factoring is the reverse of the FOIL method in these cases.
You can always check your answer by expanding what you have.

easiest way to do these problems (only applicable to quadratics or in other words highest power of 2) is using the quadratic equation.

x = ((-b) +/- (b^2 - 4ac)^0.5)/(2a) <--- note (+/- means plus or minus)
where "a" is the number in front of x squared
where "b" is the number in front of x
where "c" is the constant term.

a = 3, b = -17 (don't forget negative signs), c = 10
so plug it in the formula...
x = ((-(-17)) +/- ((-17)^2 - 4*3*10)^.05) / (2*3)
x = (17 +/- (289-120)^.05)/ 6
x = (17 +/- (169)^.05 )/ 6
x = (17 +/- 13)/6
Theres two answers for x
taking the case when we add 17 and 13: x = 30/6 = 5
taking the case when we subtract 17 and 13: x = 4/6 = 2/3
so the two solutions are x = 5 and x = 2/3 or 3x = 2
now we just get the negative of these two values...
(x-5)(3x-2) is the answer!

Answer 6

3x^2 - 17x + 10

given the problem ax^2 + bx + c = 0

x = (-b +/- sqrt(b^2 - 4 * a * c))/2a

So

x = (17 +/- sqrt(-17^2 - 4 * 3 * 10))/(2*3)
= (17 +/- sqrt (289 - 120))/6
= (17 +/- sqrt(169))/6
= (17 +/- 13)/6
= 30/6 or 4/6
= 5 or 2/3


x = (-26 +/- sqrt(676-576))/12
= (-26 +/- sqrt(100))/12
= (-26 +/- 10)/12
= -16/12 or -36/12
= -1-4/12 or -3
= -1-1/3 or -3

Answer 7

(3X-2) (x-5)

3x*x gives you 3xsquared
-5*-2=10 because two negatives give you a positive
3x*-5=-15
x*-2=-2
15+2=17


(6t+8) (t+3)
6t*t=6t squared
3*8=24
6t*3=18t
8*t=8t
18t+8t=26t

Answer 8

#1
factor first (3x-2)(x-5)
set both equal to 0 --- 3x-2=0 and x-5=0
so x equals --- 2/3 or 5

#2
factor first (6t+8)(t+3)
set both equal to 0 --- 6t+8=0 and t+3=0
so x equals --- -4/3 and -3

Answer 9

(3x-2) (x-5)