SOLUTION: Solve this question by factoring (factoring is the part that gets me) x^2+4x-3=0

Question 259293: Solve this question by factoring (factoring is the part that gets me)

x^2+4x-3=0
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
We want factors of three that add up to 4
3 only has factors 1,3 which happen to add up to 4
But there is a problem. One of the two 1 and 3 is negative but not both.
So we need factors of 3 whose difference is 4
There is a good chance you copied the signs wrong

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :

1,3

-1,-3

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .

1*(-3) = -3
(-1)*(3) = -3

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number	Second Number	Sum
1	-3	1+(-3)=-2
-1	3	-1+3=2

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

===============================================================

Answer:

So doesn't factor at all (over the rational numbers).

So is prime.

-4 and +3 would work

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :

1,3

-1,-3

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .

1*3 = 3
(-1)*(-3) = 3

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number	Second Number	Sum
1	3	1+3=4
-1	-3	-1+(-3)=-4

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

===============================================================

Answer:

So factors to .

In other words, .

Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).

RELATED QUESTIONS
Help me solve the following by factoring:... (answered by RAY100)

-x^2+4x-3 solve by... (answered by Vladdroid,lambo)

Please help me solve this equation: Find the roots by factoring. {{{ x^2-9/4x-25=0... (answered by RAY100)

Help me solve by factoring that includes the answer please {{{ 4x^2-9=0... (answered by Tatiana_Stebko)

i am really having touble factoring this x^3 + x^2 = 0. Can you show me how to solve... (answered by checkley77,solver91311)

solve by factoring given that (x+4) is one factor... (answered by josgarithmetic,ikleyn)

solve by factoring... (answered by solver91311)

Solve by factoring: 4x^2 - 1 =... (answered by Fombitz)

Solve by factoring. 4x^2 - 1 =... (answered by jim_thompson5910)