Question

Factorise: $4p^2+5pq-6p{q}^2$

Answer 1

Let us first find the HCF of all the terms of the given polynomial $4p^2+5pq-6p{q}^2$ by factoring the terms as follows:

$4p^2=2\times 2\times p\times p5pq=5\times p\times q6p{q}^2=2\times 3\times p\times q\times q$

Therefore, $HCF=p$

Now, we factor out the HCF from each term of the polynomial $4p^2+5pq-6p{q}^2$ as shown below:

$4p^2+5pq-6p{q}^2=p(4p+5q-6q^2)$

Hence, $4p^2+5pq-6p{q}^2=p(4p+5q-6q^2)$.