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: Option c) and d) are correct.

Answer 2

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

Step-by-step 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=√(9)\\x=3,-3`

x = -3 is ignored.

• 2.
  `x^2-100`

`x^2=100\\x=√(100)\\x=\pm10\\x=10,-10`

x = -10 is ignored

• 3.
  `x^2-4x+4`

To solve this we use the quadratic formula:

`(-b\pm√(b^2-4ac))/(2a)`

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

`x=(-(-4)\pm√((-4)^2-4(1)(4)))/(2* 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`