{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

M135F08A4

M135F08A4 - MATH 135 Assignment#4 Hand-In Problems Fall...

This preview shows pages 1–2. Sign up to view the full content.

MATH 135 Fall 2008 Assignment #4 Due: Wednesday 15 October 2008, 8:20 a.m. Hand-In Problems 1. For each pair a and b , state the quotient and remainder when a is divided by b . (a) a = 261, b = 12 (b) a = - 261, b = 12 (c) a = 261, b = - 12 (d) a = - 261, b = - 12 2. A quadratic equation ax 2 + bx + c = 0 (with a, b, c = 0) has real roots. Prove by contradiction that a, b, c in that order cannot be consecutive terms of a geometric sequence. 3. (a) Determine gcd(1989 , 251). (b) Determine integers x and y such that 1989 x + 251 y = gcd(1989 , 251). 4. (a) Determine gcd(686 , 511). (b) Determine integers x and y such that 686 x + 511 y = gcd(686 , 511). 5. If ac | bc and c = 0, prove that a | b . 6. Suppose that m, n P . Prove that if m 2 | n 2 , then m | n . (Hint: Use the contrapositive.) 7. Suppose a, b, n Z . Prove that if n > 0, then gcd( an, bn ) = n · gcd( a, b ). 8. (a) Determine the quotient and remainder when f ( x ) = - x 5 + x 4 + 11 x 3 - 18 x 2 + 20 x + 4 is divided by g ( x ) = x 2 - 3 x - 1. (b) Determine the quotient and remainder when f ( x ) = x 4 + 2 x 3 - 4 x 2 + x - 9 4 is divided by g ( x ) = 2 x 2 + 1.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}