Question

question 11
score: 0 of 1 point
according to the rational zero test, which values could not be zeros of the polynomial ( f(x)=x^{5}-2 x^{4}-6 x^{3}-x^{2}+8 x+30 )
a 5
b -2
c 2
d -7
e -5
f -3
g 3
h 7
submit answer attempts: 0/6
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Explanation:

Step1: Identify the constant term and leading coefficient

The polynomial is \(f(x)=x^{5}-2x^{4}-6x^{3}-x^{2}+8x + 30\). The constant term \(p = 30\) and the leading coefficient \(q=1\).

Step2: Apply the Rational Zero Theorem

The Rational Zero Theorem states that if a polynomial \(f(x)=a_{n}x^{n}+a_{n - 1}x^{n-1}+\cdots+a_{1}x + a_{0}\) has integer coefficients, then any rational zero \(r=\frac{p}{q}\), where \(p\) is a factor of the constant term \(a_{0}\) and \(q\) is a factor of the leading coefficient \(a_{n}\). Here, \(p=\pm1,\pm2,\pm3,\pm5,\pm6,\pm 10,\pm15,\pm30\) and \(q = \pm1\). So the possible rational zeros are \(r=\pm1,\pm2,\pm3,\pm5,\pm6,\pm10,\pm15,\pm30\).

Answer:

D. -7, H. 7