Factor 3x^4 + 6x^3.

Factor 3x^4 + 6x^3.

• A. 3x^4 + 6x^3
• B. 3x^3(x + 2)
• C. x^3(3x + 6)
• D. 3x^2( x^2 + 2x)

Answer: (B)

Extracting the greatest common factor. Each term shares 3x^3, so factor that out: 3x^3 is multiplied by what remains to give the original terms? 3x^4 ÷ 3x^3 = x and 6x^3 ÷ 3x^3 = 2. Therefore the expression factors to 3x^3(x + 2). This is fully factored over the integers, since x + 2 cannot be factored further. Other ways of writing it, like x^3(3x + 6) or 3x^2(x^2 + 2x), do not present the greatest common factor in a single outside product or require an extra step to reach the fully factored form, even though they’re algebraically equivalent.

Extracting the greatest common factor. Each term shares 3x^3, so factor that out: 3x^3 is multiplied by what remains to give the original terms? 3x^4 ÷ 3x^3 = x and 6x^3 ÷ 3x^3 = 2. Therefore the expression factors to 3x^3(x + 2). This is fully factored over the integers, since x + 2 cannot be factored further. Other ways of writing it, like x^3(3x + 6) or 3x^2(x^2 + 2x), do not present the greatest common factor in a single outside product or require an extra step to reach the fully factored form, even though they’re algebraically equivalent.