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Mustion 1. (a) Find the rational zeros and then the other zeros of the polynomial function f(x) = 2x3 +3x²+18x + 27, that is, solve f(x) = 0. (b) Factor f(x) into linear factors. (a) Select the correct choice below and fill in any answer box(es) within your choice. (Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) OA. There are only rational zeros and they are OB. There is only one rational zero, and the other zeros are OC. There are no rational zeros. The other zeros are (b) The factorization of f(x) into linear factors is (Type an expression using x as the variable. Use integers or fractions for any numbers in the expression.)

Mustion 1. (a) Find the rational zeros and then the other zeros of the polynomial function f(x) = 2x3 +3x²+18x + 27, that is, solve f(x) = 0. (b) Factor f(x) into linear factors. (a) Select the correct choice below and fill in any answer box(es) within your choice. (Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) OA. There are only rational zeros and they are OB. There is only one rational zero, and the other zeros are OC. There are no rational zeros. The other zeros are (b) The factorization of f(x) into linear factors is (Type an expression using x as the variable. Use integers or fractions for any numbers in the expression.)

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.5: Zeros Of Polynomial Functions
Problem 81E
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### Polynomial Factorization and Finding Rational Zeros **Problem Statement:** Given the polynomial function \( f(x) = 2x^3 + 3x^2 + 18x + 27 \), solve \( f(x) = 0 \) to find the rational zeros and other zeros of the polynomial, and factor \( f(x) \) into linear factors. **Questions:** 1. **Find the rational zeros and the other zeros if any:** - (a) Select the correct choice below and fill in any answer box(es) within your choice. - (Type an exact answer, using radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) - \(\bigcirc\) **A.** There are only rational zeros and they are \( \_\_\_ \). - \(\bigcirc\) **B.** There is only one rational zero, \( \_\_\_ \), and the other zeros are \( \_\_\_ \). - \(\bigcirc\) **C.** There are no rational zeros. The other zeros are \( \_\_\_ \). 2. **Factor \( f(x) \) into linear factors:** - (b) The factorization of \( f(x) \) into linear factors is \( \_\_\_ \). - (Type an expression using \( x \) as the variable. Use integers or fractions for any numbers in the expression.) For option B, if you select it, please provide: - One rational zero in the first blank. - The remaining zeros in the second blanks (use commas to separate multiple entries). For option C, if you select it, please provide all the non-rational zeros. **Note:** - Ensure to use exact answers, and radicals and \( i \) as needed to provide the correct zeros in the corresponding fields. - The factorization form should be \( f(x) = (x - zero1)(x - zero2)(x - zero3) \), and so on depending on how many factors are there in the polynomial.
Transcribed Image Text:### Polynomial Factorization and Finding Rational Zeros **Problem Statement:** Given the polynomial function \( f(x) = 2x^3 + 3x^2 + 18x + 27 \), solve \( f(x) = 0 \) to find the rational zeros and other zeros of the polynomial, and factor \( f(x) \) into linear factors. **Questions:** 1. **Find the rational zeros and the other zeros if any:** - (a) Select the correct choice below and fill in any answer box(es) within your choice. - (Type an exact answer, using radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) - \(\bigcirc\) **A.** There are only rational zeros and they are \( \_\_\_ \). - \(\bigcirc\) **B.** There is only one rational zero, \( \_\_\_ \), and the other zeros are \( \_\_\_ \). - \(\bigcirc\) **C.** There are no rational zeros. The other zeros are \( \_\_\_ \). 2. **Factor \( f(x) \) into linear factors:** - (b) The factorization of \( f(x) \) into linear factors is \( \_\_\_ \). - (Type an expression using \( x \) as the variable. Use integers or fractions for any numbers in the expression.) For option B, if you select it, please provide: - One rational zero in the first blank. - The remaining zeros in the second blanks (use commas to separate multiple entries). For option C, if you select it, please provide all the non-rational zeros. **Note:** - Ensure to use exact answers, and radicals and \( i \) as needed to provide the correct zeros in the corresponding fields. - The factorization form should be \( f(x) = (x - zero1)(x - zero2)(x - zero3) \), and so on depending on how many factors are there in the polynomial.
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