Question

What is the product?

Answer 1

Choice b is the answer.

Explanation:

We have given two expression.

`(2a-7)/(a).(3a^(2) )/(2a^(2)-11a+14 )`

We have to find their product.

`(2a-7)/(a).(3a^(2) )/(2a^(2)-7a-4a+14 )`

`(2a-7)/(a).(3a.a)/(a(2a-7)-2(2a-7))`

`(2a-7)/(a).(3a.a)/((2a-7)(a-2))`

`(2a-7)/(2a-7).(3a.a)/(a).(1)/(a-2)`

`(3a)/(a-2)` which is the answer.

Answer 2

Choice B is correct

Explanation:

The first step would be to factorize the expression;

`2a^(2) -11a+14`

To do this we have to determine two numbers whose product is 2(14) =28 and sum -11. By trial and error the two numbers are -7 and -4. We then substitute this two numbers in place of -11 in the expression to obtain;

`2a^(2)-4a-7a+14\\ 2a(a-2)-7(a-2)\\(2a-7)(a-2)`

The product now becomes;

`(2a-7)/(a) *(3a^(2) )/((2a-7)(a-2))\\(3a)/(a-2)`