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

1 Answer
anskat
Jun 11, 2018

# 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))#

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