How do you factor completely: #2x^2 − 28x + 98#?

1 Answer
Jul 19, 2015

Answer:

Separate out the common scalar factor, then spot a perfect square trinomial to find:

#2x^2-28x+98 = 2(x^2-14x+49) = 2(x-7)^2#

Explanation:

First separate out the common scalar factor #2# to get:

#2x^2-28x+98 = 2(x^2-14x+49)#

Then note that #x^2-14x+49# is a perfect square trinomial:

It is of the form #a^2-2ab+b^2 = (a-b)^2# with #a=x# and #b=7#

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