How do you factor (a^2 +1)^2 - 7(a^2 +1) +10(a2+1)27(a2+1)+10?

2 Answers
Sep 28, 2015

a_1=1 , a_2=-1, a_3=2, a_4=-2a1=1,a2=1,a3=2,a4=2

Explanation:

Let (a^2+1) =x(a2+1)=x
so the eqn is x^2-7x+10=0 x27x+10=0
now,
x^2 -5x-2x+10=0x25x2x+10=0
=>x(x-5)-2(x-5)=0x(x5)2(x5)=0
=>(x-2)*(x-5)=0(x2)(x5)=0
=>x-2=0 =>x=2 =>a^2+1=2 => a^2=1x2=0x=2a2+1=2a2=1
=>a=+-1 a=±1
Again,
=>x-5=0 =>x=5 =>a^2+1=5 => a^2=4x5=0x=5a2+1=5a2=4
=>a=+-2 a=±2

Sep 28, 2015

(a^2+1)^2-7(a^2+1)+10 = (a+1)(a-1)(a+2)(a-2)(a2+1)27(a2+1)+10=(a+1)(a1)(a+2)(a2)

Explanation:

Let u = a^2+1u=a2+1, then the expression is:

u^2-7u+10u27u+10 which can be factored:

(u-2)(u-5)(u2)(u5)

Replacing uu, we get:

((a^2+1)-2)((a^2+1)-5)((a2+1)2)((a2+1)5).

We can simplify to get:

(a^2-1)(a^2-4)(a21)(a24).

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

(a+1)(a-1)(a+2)(a-2)(a+1)(a1)(a+2)(a2)