Chapter 7 - Polynomial Equations and Factoring - 7.5 - Factoring x 2 + bx + c - Exercises - Page 390: 50

$(a+13b)(a-2b)$

To factor the polynomial $x^{2}+bx+c$ to $(x+p)$ and $(x+q)$, we need to have $p+q=b$ and $pq=c$. Similarly, to factor $a^{2}+11ab-26b^{2}$ to $(a+p)$ and $(a+q)$, we need to have $p+q=11b$ and $pq=-26b^{2}$ $\implies p=13b$ and $q=-2b$. Then, $a^{2}+11ab-26b^{2}=(a+13b)(a-2b)$