10.1. Represent the polynomial $(x+1)(x+2)(x+3)(x+4)+1$ as a perfect square.

## 10.2. Roots of Polynomials
10.1. The equalities $(x+1)(x+2)(x+3)(x+4)+1=x^{4}+10 x^{3}+\ldots+25$ and $\left(x^{2}+a x+b\right)^{2}=x^{4}+2 a x^{3}+\ldots+b^{2}$ show that suitable candidates are the quadratic trinomials $x^{2}+5 x \pm 5$.

Next, note that $\left(x^{2}+5 x+5\right)^{2}-1=\left(x^{2}+5 x+4\right)\left(x^{2}+5 x+6\right)$ and $x^{2}+5 x+4=(x+1)(x+4), x^{2}+5 x+6=(x+2)(x+3)$.