Monday, December 31, 2018

College Algebra, Chapter 4, 4.4, Section 4.4, Problem 32

Determine all rational zeros of the polynomial P(x)=2x3+7x2+4x4, and write the polynomial in factored form.

The leading coefficient of P is 2 and the factors of 2 are ±1,±2. They are the divisors of the constant term 4 and the factors of 4 are ±1,±2,±4. The possible rational zeros are ±1,±2,±4,±12

Using Synthetic Division







We find that 1 and 2 are not zeros but that 12 is a zero and that P factors as

2x3+7x2+4x4=(x12)(2x2+8x+8)

We now factor the quotient 2x2+8x+8 using trial and error. We get,


2x3+7x2+4x4=(x12)(2x+4)(x+2)2x3+7x2+4x4=2(x12)(x+2)(x+2)


The zeros of P are 12 and 2.

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