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The correct answer would be 2x2+ 7x + 1, 3x2 + 8    and x2 + 36. These polynomials cannot be reduced to a lower degree where the factors are integers so they should be prime. The factors are as follows:

2x2+ 7x + 1             -0.1492189406 and -3.350781059
5x2 – 10x + 5         1 and 1
3x2 + 8                     1.632993162i and - 1.632993162i
4x2 – 25                  5/2 and -5/2
x2 + 36                    6i and -6i

Equation 1 is the prime polynomials because the factors can not be found out for equation 1.

Prime Number

Any natural number that is greater than 1 and it is not a product of two smaller numbers is called the Prime Number.

The numbers with only two factors that is 1 and the number itself are Prime Numbers. For the given equations, factors are given below.

Equation 1, [tex]2x^2 +7x+1[/tex], the roots are [tex]-0.074[/tex] and [tex]-1.675[/tex].

Equation 2, [tex]5x^2 -10x+5[/tex], the factors are [tex](x-1)[/tex] and [tex](x-1)[/tex].

Equation 3, [tex]3x^2 +8[/tex], the factors are [tex](x+\dfrac {8}{3})[/tex] and [tex](x - \dfrac {8}{3})[/tex].

Equation 4, [tex]4x^2 -25[/tex], the factors are [tex](2x+5)[/tex] and [tex](2x-5)[/tex].

Equation 5, [tex]x^2 +36[/tex], the factors are [tex](x+6)[/tex] and [tex](x-6)[/tex].

Hence, equation 1 is the prime polynomials because the factors can not be found out for equation 1.

For more details about the prime numbers, follow the link given below.

https://brainly.com/question/4184435.

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