When 3x2-9x + 3 is factored, the result is 3(x2-3x + 1). why it is necessary to include the term 1 in this factored form?

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3x^2-9x+3

=3x^2-3*3x+3*1

=3(x^2-3x+1) we take 3 out from all the terms.

Last term is product of 3 and 1. When 3 is taken out, 1 is left.

why does the one have to be included though?

As mentioned above, 3 can be written as product of 3 and 1. We are taking 3 out and 1 is left. Hence, i is to be included inside the bracket as given below.

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