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

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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 :
$x^4 + 7x^2 + 10 = (x^2 +5)(x^2 + 2)$

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