# Question #f21a9

Apr 5, 2017

$\left(7 a - 2\right) \left(3 a - 5\right)$

#### Explanation:

re-arrange the expression to have the first term positive:
In this case in descending order of powers of $a$

$21 {a}^{2} - 41 a + 10$

"Find factors of $21 \mathmr{and} 10$ whose products ADD to give 41."

Note that 41 is odd, which is the sum of an odd and an even.

The largest combination of $21 \mathmr{and} 10$ is $210$
A sum of $41$ is likely to be made of combinations of $7 \mathmr{and} 3$ with $5 \mathmr{and} 2$

$\textcolor{w h i t e}{\ldots \ldots . .} 7 \text{ "2" } \rightarrow 3 \times 2 = 6$
$\textcolor{w h i t e}{\ldots \ldots . .} 3 \text{ "5" } \rightarrow 7 \times 5 = \underline{35}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} 41$

The signs in the brackets will both be negative:

$\left(7 a - 2\right) \left(3 a - 5\right)$