The other factor is (a + 2)
Solution:
Given that (a + 5) is a factor of [tex]a^2+7a+10[/tex]
To find: the other factor
Let "x" be the other factor
So both the factors "x" and (a + 5) when multiplied must give [tex]a^2+7a+10[/tex]
Therefore, we can say,
[tex]x \times (a+5) = a^2+7a+10\\\\x = \frac{a^2+7a+10}{a+5}[/tex]
Let us factor the numerator
7a in numerator can be written as 2a + 5a
[tex]x = \frac{a^2+2a + 5a+10}{a+5}[/tex]
Take "a" as common from first two terms in numerator and "5" as common from last two terms in denominator
[tex]x = \frac{a(a+2) + 5(a+2)}{a + 5}[/tex]
Take (a + 2) as common from numerator
[tex]x = \frac{(a+2)(a+5)}{(a + 5)}[/tex]
Cancel the common factors in numerator and denominator
[tex]x = a + 2[/tex]
Thus the other factor is (a + 2)
