Question

factor completely!
3x^2+10x-8

Answer 1

3x² + 10x - 8 = (x + 4)(3x - 2) <==ANSWER

You can use this pattern.

3x² + 10x - 8 Look for a GCF. There is none this time. If there was one, factor it out. Then temporarily start both parentheses with the first number and variable.
(3x.......)(3x..........) First sign goes in first parentheses.
(3x +....)(3x.........) Product of signs goes in 2nd parentheses.
(9x +....)(9x -.....) <== neg is because pos x neg = negative

Now multiply your first and third numbers together. Ignore their signs - you've already done them. 3 x 8 = 24 So, out to the side list pairs of factors of 24.

24
------
1, 24
2, 12
3, 8
4, 6

Now you want to pick which factors go in your parentheses, using these rules:

If the signs you put on your parentheses are the SAME, find the factors that ADD up to the middle number in the problem.
If the signs you put on your parentheses are the DIFFERENT, find the factors that SUBTRACT to the middle number in the problem. (Note you look at signs in the parentheses, not in the problem.)

(3x +....)(3x -.....) Your signs are different, so you want to subtract factors to get 10. Those factors are 2 and 12. When you put the numbers in the parentheses, the bigger number is pushy - it always goes first. So your factors now are:
(3x + 12)(3x - 2)

Now you have to reduce either or both parentheses by dividing each parentheses' terms by the largest possible divisor. In our problem, the first parentheses is divisible by 3 but the second parentheses does not reduce.

(3x + 12)(3x - 2)
----------
.....3
This reduces to your final factors of

(x + 4)(3x - 2) <==This is the answer to your problem.