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Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers using the appropriate multiplicities.)



P(x) = x^5 + x^4 - 21x^3 - 49x^2 + 8x + 60



x = ?



Write the polynomial in factored form.



P(x) = ?

Find all rational zeros of the polynomial Enter your answers as a comma separated list Enter all answers using the appropriate multiplicities P x x

Answer :

Final answer:

Explanation of finding rational zeros and factored form of a polynomial. Polynomial in factored form (x + 3)(x + 2)(x + 1)(x - 5)(x - 4)..

Explanation:

Find all rational zeros of the polynomial.

To find the rational zeros of the polynomial P(x) = x^5 + x^4 - 21x^3 - 49x^2 + 8x + 60, we can use the Rational Root Theorem to test possible zeros.

The rational zeros are x = -3, -2, -1, 5, 4, with multiplicities 1, 1, 1, 1, 1 respectively.

Write the polynomial in factored form. The factored form of the polynomial

P(x) = x^5 + x^4 - 21x^3 - 49x^2 + 8x + 60 is P(x)

= (x + 3)(x + 2)(x + 1)(x - 5)(x - 4).

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