How do you factor #v^2 +21v +30#?

1 Answer
George C.
Feb 20, 2017

#v^2+21v+30 = (v+21/2-sqrt(321)/2)(v+21/2+sqrt(321)/2)#

Explanation:

Complete the square then use the difference of squares identity:

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

with #a=2v+21# and #b=sqrt(321)# as follows:

#v^2+21v+30 = 1/4(4v^2+84v+120)#

#color(white)(v^2+21v+30) = 1/4((2v)^2+2(2v)(21)+(21)^2-321)#

#color(white)(v^2+21v+30) = 1/4((2v+21)^2-(sqrt(321))^2)#

#color(white)(v^2+21v+30) = 1/4((2v+21)-sqrt(321))((2v+21)+sqrt(321))#

#color(white)(v^2+21v+30) = 1/4(2v+21-sqrt(321))(2v+21+sqrt(321))#

#color(white)(v^2+21v+30) = (v+21/2-sqrt(321)/2)(v+21/2+sqrt(321)/2)#

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