Answer: 2s + 1
Step-by-step explanation:
1) Given expression: 6s² - 7s- 5 = (3s - 5) ( )
2) The missing factor ( ) is such that when it is multiplied by (3s - 5) the product is 6s² - 7s- 5.
3) Since the first term of the first factor starts with 3s, the first term of the second factor shall be 2s (since they have to yield 6s²). Then, you can write:
6s² - 7s- 5 = (3s - 5) (2s + )
4) The second term of the missing factor is positive because the product (+)(-) = (-) which is the sign of the third term of the polynomial.
5) The second term is such that when multiplied by - 5 is equal to the last term of the polynomial (also - 5), so this second terms is +1.
And you get: 6s² - 7s- 5 = (3s - 5) (2s + 1)
6) You can expand, using distributive property to confirm the result:
(3s - 5) (2s + 1 ) = (3s)(2s) + (3s)(1) - (5)(2s) -(5)(1) = 6s² - 7s- 5, which confirms the result.