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where all the ?s are integers and I don't know their values or even their signs. Now look at expanding the right side. First you multiply the two x terms to get the x^{2} term on the left which is 3x^{2}. Since 3 can only be factored as 3 × 1 I must have
Again look at expanding the right side but this time notice that the product of the two ?s must be 2 so one is positive and the other is negative. Hence there are only four possibilities.
If you expand each of the right sides you know that the x^{2} term and the constant term match the left side but only one gives the x term as x. Which one is it? Penny
Hi Melissa. Watch how I factor this example and you can follow the same steps to factor your question.
First I make my parentheses and put the x's in place:
Next I look at the number in front of the squared term. It is a 3, so I need to find two numbers that multiply to make 3. That's either 1 and 3 or 1 and 3. I'll try 1 and 3.
Now I look at the last digit. It is a 7, so two numbers that multiply to make 7 are 1 and 7. I'll try those.
The middle term of the quadratic is +4x. So I want to organize this to make +4x by moving things around and changing signs as needed.
There's no way I can make +4x by combining 1x and 21x. So I'll switch the 7 and the 1:
Now we are close, because 7x  3x makes the 4x I'm looking for. So I just need to set the minus and plus properly in the parentheses now:
To check, I use FOIL to multiply it out:
So 3x^{2} + 4x  7 factors into (1x  1) (3x + 7). There are several more questions in our archive that deal with factoring. You can look at those if you want to see more. Now you try the same steps to find the factors of 2x^{2}  3x  5, Melissa. Cheers,  


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