18. Which of the following is NOT a factor of x^4 +x^3?
Answer: D
D is NOT a factor of x^4 + x^3
The expression x^4 + x^3 can be factored as x^3(x + 1). Therefore, D, which is x^4, does not serve as a factor of the original expression.
A) X
X is a factor of x^4 + x^3 because when the expression is factored as x^3(x + 1), x is included in the x^3 term. Thus, this option is correct.
B) X + 1
X + 1 is also a factor of x^4 + x^3, as it appears in the factored form x^3(x + 1). Therefore, this option is correct.
C) X^3
X^3 is clearly a factor of x^4 + x^3, as it is part of the factored expression x^3(x + 1). Thus, this option is correct.
D) X^4
X^4 is not a factor of x^4 + x^3. Instead, x^4 is the highest degree term in the expression, but it does not appear as a separate factor in the factored form. Therefore, this option is incorrect.
Conclusion
D is definitively not a factor of x^4 + x^3, as the correct factorization shows that only x^3 and (x + 1) are factors. Options A, B, and C are all factors, confirming that D is the only choice that does not fit the criteria.