need some help for this

Question

All the real zeros of the given polynomial are integers. Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

P(x) = x3 + 6x2 − 32 Write the polynomial in factored form.

Answer 1

If written in standard form, the POSSIBLE rational zeros are plus/minus the factors of the last term divided by the factors of the first coefficient. So, in this case the last term is "32" (you can ignore the sign) and the first coefficient is "1". The factors of 32 are: 1, 2, 4, 8, 16, and 32 and the only factor of 1 is 1. So the POSSIBLE rational zeros are ± 1, 2, 4, 8, 16, and 32.

To find the zeros, start at the beginning and do synthetic division to find the zeros. The zeros will have a remainder of zero:

1 | 1 6 0 -32

| 1 7 7

----------------------

1 7 7 -25

Since the remainder is not zero, "1" is not a zero. Next try -1, then 2, then -2, and keep going until you find a zero. Once you find the zero, the quotient will be a quadratic that you can use the quadratic formula on or you can factor it to find the other two zeros..

Answer 2

Sescond post on the Rational Root Theorem.

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