How do you factor #x^2 + 8x - 19#?

1 Answer
George C.
May 12, 2016

#x^2+8x-19=(x+4-sqrt(35))(x+4+sqrt(35))#

Explanation:

Complete the square and use the difference of squares identity:

#a^2-b^2=(a-b)(a+b)#

with #a=(x+4)# and #b=sqrt(35)# as follows:

#x^2+8x-19#

#=(x+4)^2-4^2-19#

#=(x+4)^2-16-19#

#=(x+4)^2-35#

#=(x+4)^2-(sqrt(35))^2#

#=((x+4)-sqrt(35))((x+4)+sqrt(35))#

#=(x+4-sqrt(35))(x+4+sqrt(35))#

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