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.
a) x2 − 9
b) x2 −100
c) x2 − 4x + 4
d) x2 + 10x + 25
e) x2 + 15x + 36

Answer 1

X2 - 4x + 4 and x2 + 10x + 25 are both correct.

Answer 2

Answer: Option c) and d) are correct.

Explanation: Since, we know that the area of a square, $A= s^2$, where,  s is the side of a square, and it always be a positive number and makes a perfect square.

In option (a),  $x^2-9$ does not gives a perfect square for all the values of x>2, where x is a whole number. So, it can not be the area of a square.

Similarly, option (b) and (e) can not give the perfect square for all the values of x greater than 2.

But, In option (c) and (d) equations make the perfect square.

Because, $x^2+10x+25=0\Rightarrow (x+5)^2$ and this gives a perfect square for every value of x. So, it can be the area of a square.

Similarly, $x^2-4x+4=0\Rightarrow (x-2)^2$ which also gives a perfect square for every value of x. So, it also can be the area of a square.

Thus, option (c) and (d) are the correct options.