Question 1208160
<pre>
x<sup>2</sup> + 5x + 7

In order to determine whether the quadratic is prime or not, we need to decide
if it can be factorized. Any quadratic is prime if it cannot be factorized. The
quadratic in this example, x<sup>2</sup> + 5x + 7, has a leading coefficient, or
coefficient of x<sup>2</sup>, equal to 1.

This means that it is a case of simple factorization, where we need to find two
numbers with a product of +7 and a sum of +5. The sum of the two numbers needs
to be the coefficient of x. And the product of the two numbers needs to be equal
to the free term. The only product of two integers that equals 7 is 1 and 7, as
1 multiplied by 7 is equal to 7.

However, these numbers do not have a sum of 5, as 1 plus 7 is equal to 8, not 5.
As there is no pair of numbers with a product of +7 and a sum of +5, we can say
that the quadratic x<sup>2</sup> + 5x + 7 is prime and therefore cannot be factorized.

Edwin</pre>