The terms have a common factor of 2, so the first thing we do is pull that out. 2(4*x*^{2} – 28*x* + 49) Now we need to factor the part in parentheses if possible. Since the middle term has a negative sign, we hope we can factor this part like so: ▲^{2} – ■^{2} Since ▲^{2} = 4*x*^{2} and ■^{2} = 49, we need ▲ = 2*x* and ■ = 7. Squaring (2*x* – 7) does give us 4*x*^{2} – 28*x* + 49, so we can factor the original polynomial as: 2(2*x* – 7)^{2} This result was so much more satisfying than that of the last example. Like the last bite of a slice of banana cream pie. Actually, more like the first bite, because then there are still all those other bites left. |