Question

which polynomial is prime? $3x^2 - 27$, $x^2 - 25$, $2x^2 - 8$, $x^2 + 7$

Explanation:

Step1: Factor $3x^2-27$

First factor out GCF: $3(x^2-9)=3(x-3)(x+3)$

Step2: Factor $x^2-25$

Use difference of squares: $(x-5)(x+5)$

Step3: Factor $2x^2-8$

First factor out GCF: $2(x^2-4)=2(x-2)(x+2)$

Step4: Check $x^2+7$

Cannot be factored over integers.

Answer:

$x^2 + 7$