Question

3x^2+2x-8 factor


please help !!!!!!!!!!!!!

Answer 1

well here is a method that works for a quadratic

\[ax^2 + bx + c = 0\]

when you compare it to your equation, a = 3, b = 2 and c = -8

multiply a and c so 3 x -8 = -24

find the factors of -24 that add to b, which is 2.... the larger factor is positive.

any thoughts..?

Answer 2

Looking at 3x%5E2-2x-8 we can see that the first term is 3x%5E2 and the last term is -8 where the coefficients are 3 and -8 respectively.

Now multiply the first coefficient 3 and the last coefficient -8 to get -24. Now what two numbers multiply to -24 and add to the middle coefficient -2? Let's list all of the factors of -24:



Factors of -24:
1,2,3,4,6,8,12,24

-1,-2,-3,-4,-6,-8,-12,-24 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -24
(1)*(-24)
(2)*(-12)
(3)*(-8)
(4)*(-6)
(-1)*(24)
(-2)*(12)
(-3)*(8)
(-4)*(6)

note: remember, the product of a negative and a positive number is a negative number


Now which of these pairs add to -2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -2

First Number Second Number Sum
1 -24 1+(-24)=-23
2 -12 2+(-12)=-10
3 -8 3+(-8)=-5
4 -6 4+(-6)=-2
-1 24 -1+24=23
-2 12 -2+12=10
-3 8 -3+8=5
-4 6 -4+6=2





From this list we can see that 4 and -6 add up to -2 and multiply to -24


Now looking at the expression 3x%5E2-2x-8, replace -2x with 4x%2B-6x (notice 4x%2B-6x adds up to -2x. So it is equivalent to -2x)

3x%5E2%2Bhighlight%284x%2B-6x%29%2B-8


Now let's factor 3x%5E2%2B4x-6x-8 by grouping:


%283x%5E2%2B4x%29%2B%28-6x-8%29 Group like terms


x%283x%2B4%29-2%283x%2B4%29 Factor out the GCF of x out of the first group. Factor out the GCF of -2 out of the second group


%28x-2%29%283x%2B4%29 Since we have a common term of 3x%2B4, we can combine like terms

So 3x%5E2%2B4x-6x-8 factors to %28x-2%29%283x%2B4%29


So this also means that 3x%5E2-2x-8 factors to %28x-2%29%283x%2B4%29 (since 3x%5E2-2x-8 is equivalent to 3x%5E2%2B4x-6x-8)

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Answer:

So 3x%5E2-2x-8 factors to %28x-2%29%283x%2B4%29

Answer 3

wow... so using what @AllisonRoyal posted

the factors are 6 and - 4

so write the factorisation as

\[\frac{(ax + factor 1)(ax + factor 2)}{a}~~~or~~~\frac{(3x +6)(3x - 4)}{3}\]

now removed any common factors in the numerator and you'll see they(it) it will cancel with the denominator...

a fool-proof method

Answer 4

and it avoids a lot og guess and check work

Answer 5

thanks guys