Question

Find the missing factor 6s^2-7s-5=(3s-5)()

Answer 1

Answer: 2s + 1


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.