Question

Factor the polynomial below.
x^2 - 14x + 49

Answer 1

The easiest way to factor (imo) is by first checking the signs (whether or not something is positive or negative), then seeing what the factors of the last number (the one with no variable [the one with no x]). Since the second number (-14x) is negative, we know that the values that we add, whatever they are, have to result in a negative value.

Answer 2

Now, we look at the sign of the non-variable (the 49). Since its positive, we know that the factors of 49, whatever they are, have to multiply and result in a positive value------and this is key to knowing what to do next. One may only obtain a positive value if they either multiply 2 positive numbers or 2 negative numbers.

Answer 3

Keep this in mind. Remember before, how we knew that 2 values added had to equal a negative number? Well we can't obtain a negative value by added 2 positive ones, therefore, the 2 factored numbers MUST be negative.

Answer 4

Are you with me?

Answer 5

x^2 +- bx + c^2

can be recognized as a perfect square if c^2 is a square and b = 2c

here have (x-a)(x-a) = x^2 -2a + a^2 solve for a