SOLUTION: I'm stumped, can you help me answer this question? The zeros of the function f(x)=3x^2+4x-4 can be found by factoring as follows: (x+2)(3x-2) Is this True or False? Your help is

Algebra ->  Algebra  -> Functions -> SOLUTION: I'm stumped, can you help me answer this question? The zeros of the function f(x)=3x^2+4x-4 can be found by factoring as follows: (x+2)(3x-2) Is this True or False? Your help is      Log On

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 Algebra: Functions, Domain, NOT graphing Solvers Lessons Answers archive Quiz In Depth

Question 124266This question is from textbook Precalculus
: I'm stumped, can you help me answer this question?
The zeros of the function f(x)=3x^2+4x-4 can be found by factoring as follows: (x+2)(3x-2)
Is this True or False?
Your help is very well appreciated. Thank you so much.
This question is from textbook Precalculus

You can put this solution on YOUR website!

it is true
proof:
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)
In order to factor , first multiply the leading coefficient 3 and the last term -4 to get -12. Now we need to ask ourselves: What two numbers multiply to -12 and add to 4? Lets find out by listing all of the possible factors of -12

Factors:

1,2,3,4,6,12,

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

These factors pair up to multiply to -12.

(-1)*(12)=-12

(-2)*(6)=-12

(-3)*(4)=-12

Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4

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 First Number | Second Number | Sum 1 | -12 | 1+(-12)=-11 2 | -6 | 2+(-6)=-4 3 | -4 | 3+(-4)=-1 -1 | 12 | (-1)+12=11 -2 | 6 | (-2)+6=4 -3 | 4 | (-3)+4=1

We can see from the table that -2 and 6 add to 4. So the two numbers that multiply to -12 and add to 4 are: -2 and 6

breaks down to this (just replace with the two numbers that multiply to -12 and add to 4, which are: -2 and 6)

Replace with

Group the first two terms together and the last two terms together like this:

Factor a 1x out of the first group and factor a 2 out of the second group.

Now since we have a common term we can combine the two terms.

Combine like terms.
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