Answer:
b = -37
Explanation:
Given that (5x -1) is one factor of the polynomial 10x² +bx +7, you want to know the value of b.
Solution
Let the factors of the polynomial be (5x -1) and (cx -d). Then the product is ...
(5x -1)(cx -d) = 5cx² -(c+5d) +d ≡ 10x² +bx +7
Equating coefficients, we find ...
5c = 10 ⇒ c = 2 . . . . . . . coefficient of x²
d = 7 . . . . . . . . . . . . . . . constant term
Then ...
b = -(c +5d) = -(2 +5(7)) = -37
The value of b is -37.