document.write( "Question 388133: Use the rational zero theorem to find all possible rational zeros for the polynomial function. m(x)= x^3+4x^2+4x+3 \n" ); document.write( "

Algebra.Com's Answer #274475 by robertb(5830) $\"\"$ $\"About$

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Using the rational root theorem, the possible rational roots are -3, -1, 1, or 3. Now m(-1) = 2, m(1) = 12, m(3) = 78, but m(-3) = 0, so x = -3 is a (rational) root. By performing synthetic division, the quotient after dividing $\"m%28x%29=+x%5E3%2B4x%5E2%2B4x%2B3\"$ by x + 3 is $\"x%5E2+%2B+x+%2B+1\"$ , but the roots of this are complex, therefore -3 is the only rational root. \n" ); document.write( "

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