## Algebra: A Combined Approach (4th Edition)

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.
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.