Question

How do you factor the expression `36x^2 - 84x + 49`?

Answer 1

`(6x-7)^2`

Explanation:

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-7)^2`

Check FOIL
(6x-7)(6x-7)
(6x)(6x) + (6x)(-7) + (6x)(-7) + (-7)(-7)
`36x^2` - 42x - 42x + 49
`36x^2` -84 x + 49