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. Select two options. x2 − 9 x2 −100 x2 − 4x + 4 x2 + 10x + 25 x2 + 15x + 36

Answer 1

Answer: The correct answers are $x^2-9\text{ and }x^2-100$

Explanation:

To find the polynomials which could represent the are of a square having side x greater than 2, we need to find the value of 'x' for all the given polynomials.

From the given options:

• 1. $x^2-9$

$x^2=9\\x=\sqrt{9}\\x=3,-3$

x = -3 is ignored.

• 2. $x^2-100$

$x^2=100\\x=\sqrt{100}\\x=\pm10\\x=10,-10$

x = -10 is ignored

• 3. $x^2-4x+4$

To solve this we use the quadratic formula:

$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Putting values of a, b and c, we get:

$x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(4)}}{2\times 1}\\x=2,2$

As, x comes out to be 2 and is not greater than 2. Hence, this is not considered.

• 4. $x^2+10x+25$

Solving for 'x' by splitting the middle term:

$\Rightarrow x^2+5x+5x+25\\\Rightarrow x(x+5)+5(x+5)\\x=-5,-5$

Hence, this is ignored.

• 5. $x^2+15x+36$

Solving for 'x' by splitting the middle term:

$\Rightarrow x^2+12x+3x+36\\\Rightarrow x(x+12)+3(x+12)\\x=-12,-3$

Hence, this is ignored.

So, the correct polynomials are $x^2-9\text{ and }x^2-100$

Answer 2

Answer: Option c) and d) are correct.