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More Last updated date: 01st Dec 2023
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# Choose the suitable method out of middle term splitting and factor theorem to factorize the following $5{{p}^{2}}+17pq-12{{q}^{2}}$. Verified
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Hint: In this problem, we have to find the factors of the given quadratic equation. We can take the common term outside the given quadratic equation. Then we will get a simplified quadratic equation, from which we can take the constant term, which is the result of multiplying two numbers and when adding/subtracting the same two numbers, we will get the coefficient of x, those two numbers are the factors of the equation.

$5{{p}^{2}}+17pq-12{{q}^{2}}$
$\Rightarrow 17pq=20pq-3pq$
$\Rightarrow 5{{p}^{2}}+20pq-3pq-12{{q}^{2}}$
$\Rightarrow 5p\left( p+4q \right)-3q\left( p+4q \right)$
$\Rightarrow \left( 5p-3q \right)\left( p+4q \right)$
Therefore, the factors of the equation $5{{p}^{2}}+17pq-12{{q}^{2}}$ are $\left( 5p-3q \right)\left( p+4q \right)$.