Question
Factories:
$a^2-14 a-51$
$a^2-14 a-51$
✓
Answer
To factories $a^2-14 a-51$, we will find two number $p$ and $q$ such that $p+q=-14$ and $p q=-51$
Now,
$3+(-17)=-14 \text { And } 3 \times(-17)=-51$
Splittiong the middle term -14 in the given quadratic as $3 a-17 a$, we get:
$a^2-14 a-51=a^2+3 a-17 a-51$
$=\left(a^2+3 a\right)-(17 a+51)$
$=a(a+3)-17(a+3)$
$=(a-17)(a+3)$
Now,
$3+(-17)=-14 \text { And } 3 \times(-17)=-51$
Splittiong the middle term -14 in the given quadratic as $3 a-17 a$, we get:
$a^2-14 a-51=a^2+3 a-17 a-51$
$=\left(a^2+3 a\right)-(17 a+51)$
$=a(a+3)-17(a+3)$
$=(a-17)(a+3)$
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