I'm in College Algebra and it should be "easy" for me, but I'm having trouble with a particular problem.

Factor the expression completely and simplify. I'm having trouble factoring the expression.

Here it is: (a^2+1)^2-7(a^2+1)+10.

Anyone, please help me and show me step-by-step on how to factor this expression...? I understand how to simplify, but I just don't understand how to factor the expression above.

Update:

Thanks for the answer and tip, but @beeliz19, I'm sorry but the answer is wrong. Also, what confused is the minus 7 in between the parentheses. Btw, College Algebra is not the same thing as regular algebra.

Of course factoring should be easy, but I looked at the answer for this specific problem and it was a fraction with a square root on the boot. Just giving a heads up.

Update 2:

I meant square root on the *bottom

Relevance
• 7 years ago

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

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

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

a^4 + a^2 + a^2 + 1 - 7a^2 + 3

a^4 - 5a^2 + 4

You can also factor this further; let a^2 be represented by x temporarily

(x)(x) - 5(x) + 4

x^2 - 5x + 4

can be factored as

(x-4)(x-1)

Now remember how we put x in to represent a^2? Sub it back in:

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

factor further

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

can't factor further

• 7 years ago

Hint: Let u = a^2 + 1, then look at u^2 - u + 10 . Factor this and resubstitute and simplify, if possible.