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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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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.

f(x)= x^3+2x^2-5x-6

thank you

Jan 16, 2021

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According to the rational root theorem, the possible rational roots are the possibilities of the factors of the constant term divided by factors of the coefficient of the highest degree term.

Therefore, the possible roots are $$\pm1,\pm2,\pm3,\pm6$$.

You could test out these individual values and plug them into the equation.

The ones that work are -3, -1, and 2.

Therefore the factored form of this polynomial is (x+3)(x+1)(x-2)

Jan 16, 2021