Question
Factories:$a^2+14 x+45$
✓
Answer
To factories $a^2+14 x+45$, we will find two number $p$ and $q$ such that $p+q=14$ and $p q=45$
Now,
$9+5=14 \text { And } 9 \times 5=45$
Splittiong the middle term $14 x$ in the given quadratic as $9 x+5 x$, we get:
$a^2+14 x+45=x^2+9 x+5 x+45$
$=\left(x^2+9 x\right)+(5 x+45)$
$= x(x + 9) + 5(x + 9)$
$= (x + 5)(x + 9)$
Now,
$9+5=14 \text { And } 9 \times 5=45$
Splittiong the middle term $14 x$ in the given quadratic as $9 x+5 x$, we get:
$a^2+14 x+45=x^2+9 x+5 x+45$
$=\left(x^2+9 x\right)+(5 x+45)$
$= x(x + 9) + 5(x + 9)$
$= (x + 5)(x + 9)$
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