Question

Jimmy successfully factors a quadratic $4x^2 + bx + c$ as \[4x^2 + bx + c = (Ax + B)(Cx + D),\]where $A,$ $B,$ $C,$ and $D$ are integers. What are all the possible values of $A$?

Answer 1

Answer:

±1, ±2, and ±4

Step-by-step explanation:

4x² + bx + c = (Ax + B) (Cx + D)

Distribute:

4x² + bx + c = ACx² + (AD + BC) x + BD

Matching the coefficients, AC = 4.  So A must be a factor of 4.  Possible values of A are therefore ±1, ±2, and ±4.