Answer:
(7x - 5)(x + 1).
Explanation:
To factor the quadratic 7x²-2x-5, we need to find two numbers whose product is 7*(-5)=-35 and whose sum is -2.
We can start by listing the factors of 35: 1, 5, 7, 35.
Then we can look for pairs of factors whose sum is -2. We can see that -5 and 7 satisfy this condition, because -5 + 7 = 2.
Now we can rewrite the quadratic as:
7x² - 2x - 5 = 7x² + 7x - 9x - 5
= 7x(x + 1) - 5(x + 1)
= (7x - 5)(x + 1)
Therefore, the factored form of 7x²-2x-5 is (7x - 5)(x + 1).