Question: what are the factors of the expression:
![x^2+2x+1](https://img.qammunity.org/2023/formulas/mathematics/college/5j0o8x9bm8xjfsjti38znc0e8x6ca7fg84.png)
Solution:
Let the expression
![x^2+2x+1](https://img.qammunity.org/2023/formulas/mathematics/college/5j0o8x9bm8xjfsjti38znc0e8x6ca7fg84.png)
If we apply the quadratic equation:
![\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://img.qammunity.org/2023/formulas/mathematics/college/kaoalb540qnvy45obw509ttuwfskx00e99.png)
we get the zero of the polynomial
![f(x)=x^2+2x+1](https://img.qammunity.org/2023/formulas/mathematics/college/pvtc1gcojrurw3930j22g28t2vu6ein7i7.png)
which is -1. Thus the polynomial can be factored in the following way
![x^2+2x+1\text{ = (x+1)(x+1)}=(x+1)^2](https://img.qammunity.org/2023/formulas/mathematics/college/uxov8gd0mnikws023k743pu41mlz6wio38.png)
then, we can conclude that the factors of the given polynomial are:
(x+1) and (x+1)