Question

what are factors of equation - x ^2 + 1 ?​

Answer 1

Answer:

How do I factor (X^2-1)?

a²-b²

= a*a-b*b

= a*a+a*b-a*b-b*b

= a(a+b)-b(a+b)

= (a+b)(a-b)

X²–1

= (X+1)(X-1)

This is a common pattern known as the “difference of squares.”

a²−b²=(a+b)(a−b)

In your case a = x, b = 1 to give

x²−1=x²−1²=(x+1)(x−1)

You can get to this equation by working it backward. Apply FOIL to the right-hand side to get:

(a+b)(a−b)=a²−ab+ab−b²=a²−b²

Some other common patterns:

(a+b)²=a²+2ab+b²

(a+b)³=a³+3ab²+3a²b+b³

Note that the coefficients are 1,2,1 and 1,3,3,1 in the above equations. These correspond to rows in Pascal's triangle.

a²+b² can’t be factored over the real numbers. However it can be expressed using complex numbers as (a + ib)(a - ib).

There’s also a technique known as Completing the square that can be used as a shortcut for factoring quadratic polynomials.