#### Answer

Chapter 6 - Section 6.3 - Exercise Set: 97 (Answer)
For $5x^2 + 7x + c$ = $(5x + p)(x + q)$
All positive values of ‘c’ is 2.

#### Work Step by Step

Chapter 6 - Section 6.3 - Exercise Set: 97 (Solution)
Explanation :
$5x^2 + 7x + c$ = $(5x + p)(x + q)$
Since c = $p\cdot q$, for all positive ‘c’,
1) p and q have to be of the same signs
For (p + 5q) = 7
2) both p and q cannot be of negative values, hence, only positive pairs are to be considered; and
3) since p = 7 – 5q and p greater than 0, q greater than 0, q can only be equal to 1
For p = 1, q = 1 then (p + 5q) = 6 $(\neq 7)$
For p = 2, q = 1 then (p + 5q) = 7 $(= 7)$ $\Rightarrow$ c = $2\cdot1 = 2$
So, all positive values of ‘c’ is 2.