Sunday, October 8, 2017

College Algebra, Chapter 4, 4.4, Section 4.4, Problem 20

Determine all rational zeros of the polynomial P(x)=x3x28x+12, 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 12. Thus, the possible candidates are

±1,±2,±3,±4,±6,±12

Using Synthetic Division







We find that 1,3,4 and 6 are not zeros but that 2 is a zero and that P factors as

x3x28x+12=(x2)(x2+x6)

We now factor x2+x6 using trial and error, the factors are (x2)(x+3), so


x3x28x+12=(x2)(x2)(x+3)


Therefore, the zeros of P are 2 and 3.

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