How do you factor: #x^4 + 7x^2 + 10 #?

Question

5959 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-03T17:21:49

#(x^2+2)(x^2+5)#

#"the factors of + 10 which sum to + 7 are + 2 and +5"#

#rArrx^4+7x^2+10=(x^2+2)(x^2+5)#

Answer 2 · 2018-05-03T17:26:52

#x^4 + 7x^2 + 10 = (x^2 +5)(x^2 + 2)#

lets break something down a bit :
set #x^2 = a#
so #x^4 + 7x^2 + 10 = a^2 + 7a + 10#

easier?

a \/ 5
a /\ 2
5a + 2a = 7a

#therefore# #a^2 + 7a + 10 = (a+5)(a+2) = (x^2 +5)(x^2 + 2)#
so finally :
#x^4 + 7x^2 + 10 = (x^2 +5)(x^2 + 2)#