which polynomial is prime?\n3x³ + 3x² - 2x - 2\n3x³ - 2x² + 3x - 4\n4x³ + 2x² + 6x + 3\n4x³ + 4x² - 3x - 3

Explanation:

Step1: Check option 1 for factoring

Group the terms: $(3x^{3}+3x^{2})-(2x + 2)=3x^{2}(x + 1)-2(x + 1)=(x + 1)(3x^{2}-2)$.

Step2: Check option 2 for factoring

Try to factor by grouping. $(3x^{3}-2x^{2})+(3x - 4)$. There is no common - factor to factor out from each group further.

Step3: Check option 3 for factoring

Group the terms: $(4x^{3}+2x^{2})+(6x + 3)=2x^{2}(2x + 1)+3(2x + 1)=(2x + 1)(2x^{2}+3)$.

Step4: Check option 4 for factoring

Group the terms: $(4x^{3}+4x^{2})-(3x + 3)=4x^{2}(x + 1)-3(x + 1)=(x + 1)(4x^{2}-3)$.

Answer:

$3x^{3}-2x^{2}+3x - 4$