Tuesday, January 14, 2014

College Algebra, Chapter 4, 4.4, Section 4.4, Problem 18

Determine all rational zeros of the polynomial P(x)=x3+4x23x18, and write the polynomial in factored form.

The leading coefficient of P is 1, so all the rational zeros are integers:

They are divisors of the constant term 18. Thus, the possible candidates are

±1,±2,±3,±6,±9,±18

Using Synthetic Division







We find that 1 and 3 are not zeros but that 2 is a zero and that P factors as

x3+4x23x18=(x2)(x2+6x+9)

We now factor x2+6x+9 using the perfect square formula. So


x3+4x23x18=(x2)(x+3)2x3+4x23x18=(x2)(x+3)(x+3)


Therefore, the zeros of P are 2 and 3.

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