Answer to Question #158680 in Algebra for moon

Question

True or False

Write True if the statement is true and False if the statement is false. Give reasons.

1. In the division algorithm, the degree of P(x) is greater than or equal to the degree of R(x).
2. If a is a factor of the constant term of P(x), then a is a possible rational zero of P(x).
3. Every factor of P(x) is of the form (x-c), where c is the real number.
4. The remainder when P(x) is divided by D(x) is always a real number.
5. If the number of the variations in sign in P(x) is 1, then P(x) has exactly one positive real zero.
6. The number of the possible positive and negative real zeros of P(x) is never equal.

Answer 1

T - true, F - false

1) T (Division Algorithm for Polynomials)

2) F (Rational Zeros Theorem)

3) T (Remainder Theorem)

4) T (we never get $\sqrt{-1}$ when dividing)

5) F (Rational Zeros Theorem)

6) F (Upper and Lower Bound Tests for Real Zeros)