HW7 - MAP 103: Proficiency Algebra Homework #7 DUE:...

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Unformatted text preview: MAP 103: Proficiency Algebra Homework #7 DUE: THURSDAY, OCTOBER 22, 2009 1. Factor each of the following polynomials using “trial and error.” (a) 3x2 + 15x + 4 (b) 7x2 − 6x − 7 2. Factor each of the following polynomials using grouping. (a) 3x3 − 9x2 + 6x − 18 (b) 1 + x + xy + y 3. Factor each of the following polynomials using substitution. (a) (x + 1)2 − 10(x + 1) + 9 (b) (x − 1)4 − (x − 1)2 4. Use the Rational Root Test to find one factor in the form x − c or x + c for the given polynomials. (a) 6x5 + 7x4 + 3x3 − 10x2 + 20x + 50 (b) 4x7 − 6x5 + 2x + 8 5. Find the quotient and remainder (if any) using long divison. Show all work. Make sure if powers are missing to insert place holders, i.e. 0xmissing power . 2x4 − 5x3 + 7x2 + 3 (a) x−4 x6 − x4 − x2 − 1 (b) x+1 6. Find the greatest common divisor, gcd(p, q ), of the polynomials, p and q, given below. (a) p = x3 + 1, q = x2 + x − 1 (b) p = x4 + x3 − x − 1, q = x3 − 2x2 + 2x − 1 7. Use the Rational Root Test in concert with the Remainder/Factor Theorem to write the given polynomials as a product of linear factors. (a) x4 − 10x3 + 35x2 − 50x + 24 (b) x6 + 3x5 − 3x4 − 15x3 − 6x2 + 12x + 8 8. Find the sum of the two rational expressions. Express in simplest form when possible. 1 x (a) x+1 + x+2 x−1 x (b) x+2 + x+4 9. Find the difference of the two rational expressions. Express in simplest form when possible. 2x−1 (a) (x+2)(x−1) − (x−x+1+1) 1)(x 2 1 (b) x2 +7x+6 − x−1 10. Find the product of the two rational expressions. Express in simplest form when possible. 2 2 x−1 x2 −20 (a) x2x +x+20 · 3x+xx−2 2+ +9 (b) x4 +17x2 +16 x4 −2x2 +1 · x4 −1 x4 +3x2 +2 ...
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This note was uploaded on 04/18/2010 for the course MAP 103 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.

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