Factor polynomials that can be factored as the product of a monomial and a quadratic expression, then further factor the quadratic expression.

Problem

The quadratic expression x, start superscript, 2, end superscript, minus, 4, x, plus, M can be factored as left parenthesis, x, plus, g, right parenthesis, left parenthesis, x, plus, h, right parenthesis, where M, g, and h are integers.
Pat wrote that M could be equal to minus, 14.
Grace wrote that M could be equal to minus, 12.
Which student is correct ?
Please choose from one of the following options.