Question

Jimmy is trying to factor the quadratic equation $ax^2 + bx + c = 0.$ He assumes that it will factor in the form \[ax^2 + bx + c = (Ax + B)(Cx + D),\]where $A,$ $B,$ $C,$ and $D$ are integers. If $a = 4,$ and Jimmy wants to find the value of $A,$ what are the possible values he should check, in order to find $A$?

Answer 1

Answer:

possible value of A are 1, 2, 4

Step-by-step explanation:

Jimmy is trying to factor the quadratic equation ax^2 + bx + c = 0.

He assumes that it will factor in the form ax^2 + bx + c = (Ax + B)(C x + D)

Given a=4

We need to find the value of A

When we do factoring we use the factors of the numbers

(Ax+B)(Cx+D) is ACx^2 + ADx + BCx + BD

$ax^2 + bx + c =ACx^2 + ADx + BCx + BD$

When a=4  then AC is also 4

A* C = 4

1 * 4= 4

2 * 2= 4

4 * 1 = 4

So possible value of A are 1, 2, 4

Answer 2

If

$ax^2+bx+c=(Ax+B)(Cx+D)$

then

$ax^2+bx+c=ACx^2+(AD+BC)x+BD$

$\implies a=AC$

If $a$ is known and Jimmy wants to find $A$, then he has to know the value of $C$.