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We are trying to factor 3x2 +5x+2.
First of all, we see there is no number or powers of x that can be factored out of all three terms.
So we try and factor it as the product of binomials.
There are only 2 factors of 3, those being 3 and 1. Same with 2, the factors are 2 and 1.
Also, the signs are both positive so we need only consider (ax+b)(x+c). No need to worry about the negatives since that is not possible
So try (3x+1)(x+2)=3x2 +x+6x+2. We have 7x and that does not work
Now try (3x+2)(x+1)=3x2 +2x+3x+2=3x2 +5x+2
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