Solve: q^2-10 p+21 - Vidyadip

Question

Solve:
$q^2-10 p+21$

✓

Answer

$q^2-10 p+21$
$= q ^2-10 q +\left(\frac{10}{2}\right)^2-\left(\frac{10}{2}\right)^2+21$ [Adding and subtracting $\left(\frac{10}{2}\right)^2$, that is $5^2$ ]
$=q 2-2 \times q \times 5+5^2-5^2+21$
$=(q-5) 2-4$ [ completing the square]
$=[(q-5)-2][(q-5)+2]$
$=(q-5-2)(q-5+2)$
$=(q-7)(q-3)$

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