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

2 Answers
Mar 5, 2018

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

Mar 5, 2018

#(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)#