Question

$15ab(a^2-7a+10)÷3b(a-2)$

• A. $5a(a-5)$
• B. $5a(a+5)$
• C. $a(a-5)$
• D. None

Answer 1

The correct option is A $5a(a-5)$

• Let us first factorize $(a^2-7a+10)$ as follows:

$a^2-7a+10=a^2-5a-2a+10=a(a-5)-2(a-5)=(a-2)(a-5)$

Since we have to divide $\frac{15ab(a^2-7a+10)}{3b(a-2)}$, therefore, we will divide $\frac{15ab(a-2)(a-5)}{3b(a-2)}$ as shown below:

$\frac{15ab(a-2)(a-5)}{3b(a-2)}=\frac{15}{3}\times \frac{ab(a-2)(a-5)}{b(a-2)}=\frac{3\times 5}{3}\times a(a-5)=5a(a-5)$

Hence, $\frac{15ab(a^2-7a+10)}{3b(a-2)}=5a(a-5)$.