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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

Verified Answer :

antonsandiego

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.

frika

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.

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