How do you factor the expression #36x^2 - 84x + 49 #?
To factor this expression, first notice that the first and last coefficients (the numbers multiplying the variable; for example the coefficient of 64x is simply 64) are perfect squares. 36 is 6 squared and 49 is 7 squared. Although there could be other combinations, this is the most likely one because it is neat and simple. So the factored form now looks like this: (6x ? 7)(6x ? 7) where the question mark represents a plus or minus sign. Since the middle term determines whether the sign is positive or negative, look at it. -84x indicates the signs should be both negative because that is the only way to get a middle negative term and a positive last term. So that yields (6x-7)(6x-7) or simplified:
(6x)(6x) + (6x)(-7) + (6x)(-7) + (-7)(-7)