Answer:
B
Explanation:
a prime polynomial is one which does not factor into 2 binomials.
its only factors are 1 and itself
attempt to factorise the given polynomials
3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )
= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(3x² - 2) ← in factored form
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3x³ - 2x² + 3x - 4 ( factor the first/second terms
= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored
thus this polynomial is prime
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4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )
= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term
= (2x + 1)(2x² + 3) ← in factored form
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4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )
= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(4x² - 3) ← in factored form
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the only polynomial which does not factorise is
3x³ - 2x² + 3x - 4