F(x)=x^3+5x^2-17x-21 - Math Homework Answers

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f(x)=x^3+5x^2-17x-21
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use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.
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asked Oct 2, 2013 in Algebra 2 Answers by answer comment

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f(x)=x^3+5x^2-17x-21 1. factors of constant: 21: 1,3,7,21 2. factors of first coefficient: 1 3. p/q is 1,-1,3,-3,7,-7,21,-21 4. use synthetic division: 1 | 1 5 -17 -21 |_____1_____4______-13____ 1 4 -13 8 not a factor -1 | 1 5 -17 -21 |____-1___-4___-13_______ 1 4 13 8 not a factor 3 | 1 5 -17 -21 |____3___6___-69____ 1 2 -23 not a factor -3 | 1 5 -17 -12 |____-3__-24__-21________ 1 8 7 9 not a factor 7 | 1 5 -17 -21 |_____7__-14_-21________ 1 -2 -3 0 this is a factor -7 | 1 5 -17 -21 |____-7___-84_________ 1 12 not a factor 21 | 1 5 -17 -21 |___21____________ 1 -16 not a factor -21 | 1 5 -17 -21 |___-21____________ 1 26 not a factor 7 is the real root. answered Oct 2, 2013 by Level 10 User (55.7k points) ask related question comment

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