How do you factor (a^2 +1)^2 - 7(a^2 +1) +10?

2 Answers
Sep 28, 2015

a_1=1 , a_2=-1, a_3=2, a_4=-2

Explanation:

Let (a^2+1) =x
so the eqn is x^2-7x+10=0
now,
x^2 -5x-2x+10=0
=>x(x-5)-2(x-5)=0
=>(x-2)*(x-5)=0
=>x-2=0 =>x=2 =>a^2+1=2 => a^2=1
=>a=+-1
Again,
=>x-5=0 =>x=5 =>a^2+1=5 => a^2=4
=>a=+-2

Sep 28, 2015

(a^2+1)^2-7(a^2+1)+10 = (a+1)(a-1)(a+2)(a-2)

Explanation:

Let u = a^2+1, then the expression is:

u^2-7u+10 which can be factored:

(u-2)(u-5)

Replacing u, we get:

((a^2+1)-2)((a^2+1)-5).

We can simplify to get:

(a^2-1)(a^2-4).

Each of these is a difference of squares, so we can finish with:

(a+1)(a-1)(a+2)(a-2)