The given polynomial, 6•x² + 12•x + 6, can be factored by rearranging and looking for the common factors to give;
6•x² + 12•x + 6 = 6•(x + 1)²
How can the given polynomial be factored?
The given polynomial is presented as follows;
6•x² + 12•x + 6
The coefficients in the terms and the constant have a common factor of 6, which gives;
6•x² + 12•x + 6 = 6•(x² + 2•x + 1)
x² + 2•x + 1 = x² + x + x + 1
x² + x + x + 1 = x•(x + 1) + 1•(x + 1)
x•(x + 1) + 1•(x + 1) = (x + 1)•(x + 1) = (x + 1)²
Therefore;
x² + 2•x + 1 = (x + 1)²
6•(x² + 2•x + 1) = 6•(x + 1)²
6•x² + 12•x + 6 = 6•(x² + 2•x + 1)
Therefore;
- 6•x² + 12•x + 6 = 6•(x + 1)²
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