So is a linear polynomial with rational coefficients. P(x) is a 4th degree polynomial. The graph of has exactly three distinct x-intercepts. Part A Which polynomial could be P(x)? A. B. C. D. Part B For one of the polynomials above, explain why it could not be P(x). Proposition 1 The sum of two linear polynomials with integer coefficients is always a linear polynomial with integer coefficients. The outline of a proof of Proposition 1 is shown. Add one or more justifications for steps 3, 4, and 5 of the proof from the list of justifications below. The Closure of the Integers Under Addition The sum of two integers is always an integer The Commutative Property If A and B are real numbers, then A + B = B + A The Associative Property If A, B, and C are real numbers, then (A + B) + C = A + (B + C) The Distributive Property If A, B, and C are real numbers, then A(B + C) = AB + AC The Any-Order Property of Addition The sum of two or more real numbers can be performed in any order or any grouping. Statement Justification Given and where a, b, c, and d are integers. Hypothesis By Definition
So is a linear polynomial with rational coefficients. P(x) is a 4th degree polynomial. The graph of has exactly three distinct x-intercepts. Part A Which polynomial could be P(x)? A. B. C. D. Part B For one of the polynomials above, explain why it could not be P(x). Proposition 1 The sum of two linear polynomials with integer coefficients is always a linear polynomial with integer coefficients. The outline of a proof of Proposition 1 is shown. Add one or more justifications for steps 3, 4, and 5 of the proof from the list of justifications below. The Closure of the Integers Under Addition The sum of two integers is always an integer The Commutative Property If A and B are real numbers, then A + B = B + A The Associative Property If A, B, and C are real numbers, then (A + B) + C = A + (B + C) The Distributive Property If A, B, and C are real numbers, then A(B + C) = AB + AC The Any-Order Property of Addition The sum of two or more real numbers can be performed in any order or any grouping. Statement Justification Given and where a, b, c, and d are integers. Hypothesis By Definition