Factorize the expressions and divide them as directed:

15ab (a²–7a + 10) ÷ 3b (a – 2)

In the given term

Dividend = 15ab (a²–7a + 10)

The given expression (a²–7a + 10) looks as

x² + (a + b) x + ab

where a + b = -7; and ab = 10;

factors of 10 their sum

-1 × -10 -1-10 = -11

-2 × -5 -2-5 = -7

∴ the factors having sum -7 are -2 and -5

(a²–7a + 10) = a² + (-2-5)a + 10

= a²–5a – 2a + 10

= a(a – 5) – 2(a – 5)

= (a – 5)(a – 2)

Divisor = 3b (a – 2)

=

= 5a(a – 5)

Hence dividing 15ab (a²–7a + 10) by 3b (a – 2) gives out 5a(a – 5)