In each of the problems, three statements are given. Two of them agree to each other, and one of the statements contradicts with the other two. Identify the contradictory statement.

For each problem:

- Identify the contradictory statement.

- explain why it is contradictory to the other two.

- describe how to transform him in contradictory to agree with the other two.

1-

Statement 1: x^3-7x+6/x+4 = x^2-4x+9 - 30/x+4

Statement2: -4 is a root of the polynomial f(x)^3-7x+6

Statement3: f(x)^3-7x+6 f(-4)=-30

2-

Statement1: The polynomial f(x)^3-x^2-25x-12 has exactly three rational roots: x=-3, x=-1/2,

Statement2: According to the rational root theorem, the possible rational roots of the polynomial f(x)^3-x^2-25x-12 are +-1/2, +-1, +-3/2, +-2, +-3, +-4, +-6, +-12.

Statement3: By synthetic division 5 2 -1 -25 -12 10 45 12

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2 9 7 0

3- Now you need to create one problem

- Write three statements about roots of polynomials. Two of the statements should agree

with each other. The third statement should contradict the other two.

-Identify the contradictory statement.

-Write at least two sentences to explain why the third statement is contradictory.

-Write at least two sentences to explain how the contradictory statement could be fixed to

make it agree with the other two