Question

If f(-1) for the polynomial f(x) = 2x^4 + 32x^3 - 5 is -2, can you use the Factor Theorem to find the other factor? Yes, because (x + 1) is a factor of all degree 4 polynomials.

a) True
b) False

Answer 1

The given statement claiming that Factor Theorem implies (x + 1) is a factor of all degree 4 polynomials is false since Factor Theorem applies only when f(c) = 0 for the polynomial f(x).

Step-by-step explanation:

The student has asked whether Factor Theorem can be used to find another factor if f(-1) for the polynomial f(x) = 2x^4 + 32x^3 - 5 is -2. The statement provided in the question, 'Yes, because (x + 1) is a factor of all degree 4 polynomials,' is false. The Factor Theorem states that if f(c) = 0 for a polynomial f(x), then (x - c) is a factor of that polynomial. In this case, because f(-1) ≠ 0, (x + 1) is not a factor of f(x). Thus, the given reasoning is incorrect, and the Factor Theorem cannot be applied this way.