SOLUTION: Factor the given polynomial X^2+4x+3= Is this polynomial a prime or can it be sloved. Also can someone break this down for me so I can see how to work it. Thanks

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor the given polynomial X^2+4x+3= Is this polynomial a prime or can it be sloved. Also can someone break this down for me so I can see how to work it. Thanks      Log On


   

Question 760604: Factor the given polynomial
X^2+4x+3=
Is this polynomial a prime or can it be sloved. Also can someone break this down for me so I can see how to work it. Thanks
Found 3 solutions by Stitch, josgarithmetic, Alan3354:
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
First find the factors of 1 from the X%5E2
The factors of 1 are: 1,1
Next Find the factors of 3 (the constant)
The factors of 3 are: 1,3
Note that the 3 is positive that means that the factors have to both be positive or both negative.
Now use the factors of 1 and the factors of 3 to come up with the 4X
1*3 + 1*1 = 4
So X%5E2+%2B+4X+%2B+3 can be rewritten as %28X+%2B+3%29%2A%28X+%2B+1%29
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Now we have to solve for each part of the equation.
The equation equals zero when either of the parentheses equal zero.
X+%2B+3+=+0
Subtract 3 from both sides
highlight%28X+=+-3%29
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X+%2B+1+=+0
Subtract 1 from both sides
highlight_green%28X+=+-1%29

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
You are looking for two numbers, h and k, so that hk=3 and h+k=4. You need for h and k to be rational numbers or preferably integers. Based on the signs in the given polynomial, both h and k must be positive. Your only choice (for integers) is 3 and 1 which will work.

Another structuring of the search:
%28x%2Bh%29%28x%2Bk%29=?
x%5E2%2Bhx%2Bkx%2Bhk
x%5E2%2B%28h%2Bk%29x%2Bhk
How can x%5E2%2B%28h%2Bk%29x%2Bhk=x%5E2%2B4x%2B3 ?


x%5E2%2B4x%2B3 is factorable.
If let h=3, and k=1, then you have
highlight%28%28x%2B1%29%28x%2B3%29%29
Because 3*1=3 and 1+3=4

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Factor the given polynomial
X^2+4x+3=
Is this polynomial a prime or can it be sloved.
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It's not an equation, so there's nothing to solve.
It says factor.
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Find a pair of factors of 3 that add to 4.
It's all positive, makes it easier.