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Factorise x² + 4x + 3.

I understand everything perfectly until I have to split the two sections, add up and pull out the common factors:

x² + 3x: common factor is x
1x + 3: common factor is 1

From here I do not understand how you get to the answer which I do know is (x + 1) • (x + 3).

None of the explanations out there give detail to this step. I don’t understand how adding those two groups up (while pulling out common factors) will give you (x + 1) • (x + 3)!

I would hugely appreciate any help on this! Thank you :)

1 Answer

5 votes
Ok so from the x^2 + 3x if you take out the common factor, you would be left with (x+3) and then the left over x. and from the 1x+3, if you take out the 1 you will just be left with (x+3). Since the (x+3) is the common factor of the two equations that will be one of the factors, and the leftover and 1 will form another factor of (x+1). Making the factor (x+3)(x+1). But there's also other ways of factoring if it's too confusing, what I do is find numbers that multiply to make 3. This would be 1 and 3 since 1x3=3. Since both of the parts in the polynomial is positive the factors would both be positive. To check to see if the numbers are going to be right you can add up the multiples, so 3 and 1, 3+1 would be 4. After you check that you can factor them (x+1)(x+3) the order doesn't matter. This is just the way that I do it.
User Val Nolav
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