OG详解-OG4 数学1 Q23

Choice D is correct. It’s given that 4x² + bx -45 can be rewritten as (hx + k)(x + j). The expression (hx + k )(x + j) can be rewritten as hx² + jhx + kx + kj , or hx² +( jh + k )x + kj . Therefore, hx² +( jh + k )x + kj is equivalent to 4x² + bx -45. It follows that kj =-45. Dividing each side of this equation by k yields j = −45k​​. Since j is an integer, - ​45k​ must be an integer. Therefore,  ​45k​ must also be an integer.
Choice A is incorrect and may result from conceptual or calculation errors. 
Choice B is incorrect and may result from conceptual or calculation errors. 
Choice C is incorrect and may result from conceptual or calculation errors.