Question

Which polynomials, given in square inches, could represent the area of a square with whole number side lengths if x is a whole number greater than 2? Remember, the formula for the area of a square is A = s2. CHECK ALL THAT APPLY.

~ x2 − 9
~x2 −100
~x2 − 4x + 4
~x2 + 10x + 25
~x2 + 15x + 36

Answer 1

I checked every polynimial using the formula of a square given by you. And I think there is more than one right option. There are two right polinomials. ~x2 − 4x + 4; ~x2 + 10x + 25. They are both applies to the task given above as I checked each polynomial by myself.

Answer 2

You can simplify two of these polynomials, using formulas for perfect square trinomials:

$(a+b)^2=a^2+2ab+b^2,\\(a-b)^2=a^2-2ab+b^2$.

Then,

$x^2 - 4x + 4=(x-2)^2$,

$x^2 + 10x + 25=(x+5)^2$.

You can also factorize all polynomials that left:

$x^2-9=(x-3)(x+3)$,

$x^2 -100=(x-10)(x+10)$,

$x^2 + 15x + 36=(x+12)(x+3)$.

If x is a whole number greater than 2, then:

1. polynomial $x^2 - 4x + 4=(x-2)^2$ can represent the area of a square with whole number side lengths equal to x-2.

2. polynomial $x^2 +10x + 25=(x+5)^2$ can represent the area of a square with whole number side lengths equal to x+5.

3. polynomial $x^2 - 9$ can represent the area of a square with whole number side lengths 4 (when x=5, then $x^2 - 9=25-9=16$).

4. polynomial $x^2 - 100$ can represent the area of a square with whole number side lengths 24 (when x=26, then $x^2 - 100=676-100=576$).

5. polynomial $x^2 + 15x + 36=(x+12)(x+3)$ can't represent the area of a square with whole number side lengths.