Final answer:
The greatest common factor of the polynomial 3r³ – 6r is 3r, factoring out which yields a) 3r(r² – 2). The correct answer is option a, and the factored polynomial can be checked by multiplying the factors back together to ensure accuracy.
Step-by-step explanation:
The subject of this question is factoring a polynomial. We are asked to factor out the greatest common factor (GCF) from the given polynomial 3r³ – 6r. The GCF of 3r³ and 6r is 3r, because both terms are divisible by 3r. When we divide both terms by 3r, we're left with r² from the first term and 2 from the second term (taking into account the negative sign). This gives us the factored form:
3r(r² – 2)Hence, the correct answer is option a. 3r(r² – 2). It is important to always check if the factored form multiplies back to the original polynomial to confirm that the factoring is correct. In this case, 3r × r² equals 3r³ and 3r × (– 2) equals – 6r, matching the original polynomial.