Find all real zeros
asked Nov 15, 2017 in Algebra 2 Answers by anonymous

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1 Answer

Try x=-1: 1-3-3+11-6=0 so x+1 is a factor.

Use synthetic division to find the cubic:

-1 | 1  3 -3 -11  -6

      1 -1 -2    5 | 6

      1  2 -5   -6 | 0 = x³+2x²-5x-6

The constant -6 has to be the product of factors. So if we take x=2, the cubic becomes 8+8-10-6=0, so x-2 is a factor. Use synthetic division to find the quadratic.

2 | 1 2 -5  -6

     1 2  8 | 6

     1 4  3 | 0 = x²+4x+3 = (x+3)(x+1)

Full factorisation: (x+1)²(x-2)(x+3). The zeroes are -1, 2 and -3.

 

answered Nov 15, 2017 by Rod Top Rated User (571,080 points)

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