(10 points) Prove uniqueness. That is, if r1 and r2 are both remainders after the division of b by a, then r1 = r2. You can use without proof reasonable facts about integer multiplication, addition, subtraction, and >, but don’t assume anything about integer division. In particular, you can use the fact that there are no integer multiples of a that are greater than 0 and less than a. Hint: Use proof by contradiction combined with proof b

Write the sentence as an equation. z plus 372 is equal to 160

Use addition and subtraction to simplify the following polynomials. a. add polynomials: (3 – 4x + 8x^2) + (–6 + 2x – 5x^2) step 1: rewrite the polynomials without the parentheses. step 2: write the polynomial in descending order and use parentheses around like terms. step 3: add the like terms identified in step 2 to simplify the polynomial. b. subtract polynomials: (3x – 5 – 7x^2) – (–2 + 6x^2 – 5x) step 1: rewrite the polynomials without the parentheses. remember to multiply each term in the second parentheses by –1. show your work. step 2: write the polynomial in descending order and use parentheses around like terms. step 3: add the like terms identified in step 2 to simplify the polynomial.

What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4? 1 –1 i –i