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 $A$?

The possible values of A are 1, 2 and 4

The factorized expression is given as:

Open both brackets

By comparison, we have:

means that, the possible values of A are the factors of 4, because A and C are integers.

The factors of 4 are 1, 2 and 4

Hence, the possible values of A are 1, 2 and 4

Read more about factorized expressions at:

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±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.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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