Question

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

Answer 1

`(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)`

Answer 2

`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)`