Factorise the following quadratic polynomial by splitting the middle term:
$6 x^{2}+7 x-20$

(A) To factorise $6 x^{2}+7 x-20$ by splitting the middle term,we need to find two numbers whose product is $6 \times (-20) = -120$ and whose sum is $7$.
These two numbers are $15$ and $-8$,since $15 \times (-8) = -120$ and $15 + (-8) = 7$.
Now,rewrite the middle term $7x$ as $15x - 8x$:
$6 x^{2} + 15 x - 8 x - 20$
Group the terms to factor out common factors:
$(6 x^{2} + 15 x) - (8 x + 20)$
$3 x(2 x + 5) - 4(2 x + 5)$
Taking $(2 x + 5)$ as a common factor:
$(2 x + 5)(3 x - 4)$