Question

Which of the following about $x^2+9$ is true?

• A. $x^2+9$ cannot be split into the product of first degree factors.
• B. $x^2+9$ can be split into the product of first degree factors.
• C. We cannot determine if we can find factors
• D. $x^2+9$ is an equation

Answer 1

The correct option is A

$x^2+9$ cannot be split into the product of first degree factors.

Let the first degree factors as (x-a)(x-b).

Then, we have

$x^2+9=(x-a)(x-b)=x^2-(a+b)x+ab$

The above expression gives a+b=0

ab=9

We need to find "a" and "b". For that we need to find (a-b) first using the formula $(a-b{)}^2=(a+b{)}^2-4ab$

$\Rightarrow (a-b{)}^2=0-4(9)=-36$

The square of no number is negative. So, there are no numbers satisfying the above pair of equations.

Thus $x^2+9$ cannot be split into the product of first degree factors.