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Question What are the rational zeros of the function $f(x) = x^3 - x^2 - 17x - 15$? List the values separated by commas. Provide your answer below: $x = \Box$

          Question
What are the rational zeros of the function $f(x) = x^3 - x^2 - 17x - 15$? List the values separated by commas.
Provide your answer below:
$x = \Box$

question what are the rational zeros of the function fx x3 x2 17x 15 list the values separated by commas provide your answer below x box 04479

Added by Gloria C.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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Solved by Expert Adi S

11/21/2023

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We need to find the rational zeros of the polynomial function $f(x) = x^3 - x^2 - 17x - 15$. Show more…

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Question What are the rational zeros of the function $f(x) = x^3 - x^2 - 17x - 15$? List the values separated by commas. Provide your answer below: $x = \Box$

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Transcript

00:01 In this question, the given function fx is equal to x cube plus 9x square minus 7x minus 15.

00:09 Now, considering the factor of the constant term minus 15 dividing by the factors leading coefficient 1, possible rational zeros of this function are plus minus 1, comma plus minus 3, comma plus minus 5, comma plus minus 15.

00:30 Now, these are the zeros according to the rational zero theorem, which is the answer of the first part.

00:39 Now, in the second part, to test the possible rational zeros, test possible rational zeros.

00:48 We will use synthetic division.

00:56 So testing for x is equal to 1.

01:00 Now, the coefficients are 1, 9, minus 7 and minus 15.

01:07 Now testing with the 1, we get 1, 10 and 3.

01:12 Since the remainder is not zero, so x1 is equal to 1 is not a zero of this equation.

01:24 Now testing with the x is equal to minus 1.

01:29 Now again, the coefficients are 1, 9, minus 7, minus 15.

01:35 So with minus 1, we will get 1, 8 and 15.

01:41 So the remainder again is not equal to zero.

01:45 So x is equal to minus 1 is not a zero of this equation.

01:52 Now at number 3, testing with x is equal to 3, the coefficients are 1, 9, minus 7, 15 and testing with 0 will give us 1 under 9, 12 under minus 7 and 15 under minus 15...

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