# Can any anyone explain how #x^2+4x+2# become #(x-sqrt2+2)(x+sqrt2+2)# #x^2+4x+2=(x-sqrt2+2)(x+sqrt2+2)# helppppp??

##### 3 Answers

We know that if

In order to factorize a degree two polynomial, we can use the quadratic formula suposing that

But

To check the solution we can multiply both factors and the result must be the initial polynomial

Hope this helps

#### Explanation:

#"given "x=a" is a root of a polynomial then"#

#(x-a)" is a factor of the polynomial"#

#"find the roots using the "color(blue)"quadratic formula"#

#"with "a=1,b=4" and "c=2#

#x=(-4+-sqrt(16-8))/2=-2+-sqrt2#

#"thus factors are"#

#(x-(-2-sqrt2))" and "(x-(-2+sqrt2))#

#(x+sqrt2+2)" and "(x-sqrt2+2)#

#rArrx^2+4x+2=(x+sqrt2+2)(x-sqrt2+2)#

Kindly refer to **Explanation.**

#### Explanation:

**Completing the square** of the **quadr. poly.**

**as desired!**