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

2 Answers
May 3, 2018

Answer:

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

Explanation:

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

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

May 3, 2018

Answer:

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

Explanation:

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)#