Question

How do you factor `x+1+2x^2`?

Answer 1

`x+1+2*x^2=(x+(1/2+-sqrt(2)/(2)))*(x-(1/2+-sqrt(2)/(2))`

Explanation:

The Quadratic Formula: For `ax^2" + bx + c = 0`, the values of x (factors) which are the solutions of the equation are given by:
`x=(b+-sqrt(4*a*c))/(2*a)`

Here, a=2, b=1 and c=1, so
`x=(1+-sqrt(4*2*1))/(2*2)`

`=(1+-2*sqrt(2))/(4)`

`=1/2+-sqrt(2)/(2)`

You can then factor as follows, using the two factors found:

`-> x+1+2*x^2=(x+(1/2+-sqrt(2)/(2)))*(x-(1/2+-sqrt(2)/(2))`