Question

How do you factor the trinomial `1-14x+49x^2`?

Answer 1

`1 - 14x + 49x^2 = (1 - 7x)(1 - 7x) = (1 - 7x)^2 = (7x - 1)^2`

Answer 2

`(x-7)(x-7)`

Explanation:

`1-14x+49x^2`

The information you need to find the factors is contained in the terms of this quadratic trinomial:

• there are `3` terms in ascending powers of `x`
  the factors will be `(x???)(x???)`

• we need to find factors of `49` which ADD to make `14`
  (the sign of `49` is positive `rarr` ADD)

• `7xx7 = 49 and 7 +7 = 14`
  The factors will be `(x?7)(x?7)`

The positive sign of `49` indicates that the signs in the brackets must be the SAME becasue `+xx+ = + and -xx- = +`

The sign of the middle term `-14x` indicates that the signs will be negative.

`(x-7)(x-7)`