Explanation Given Information: The provided polynomial is 18 x 3 − 9 x 2 − 8 x + 4 . Formula used: Rational Zeros Theorem: If a polynomial ( a n x n + a n − 1 x n − 1 + ⋯ + a 1 x + a o ) has integer coefficient, then every rational zero is of the form x = p q , where p is a factor of a o , and q is a factor of a n . Calculation: Consider the polynomial, p ( x ) = 18 x 3 − 9 x 2 − 8 x + 4 Factor of constant term ( 4 ) of polynomial 18 x 3 − 9 x 2 − 8 x + 4 will be ± 1 , ± 2 and ± 4 . Factor of leading coefficient ( 18 ) will be ± 1 , ± 2, ± 3 , ± 6 and ± 18 . Now apply, Rational Zeros Theorem for polynomial p ( x ) to find zeros. The possible rational zeros are the factor of the constant term divided by the factors of the leading coefficient that is, ± 1 , ± 1 2 , ± , 1 6 ± , 1 3 , ± 1 9 , ± 2 9 , ± 4 9 , ± 2, ± 4 and ± 1 18 The possible rational factor of polynomial 18 x 3 − 9 x 2 − 8 x + 4 is ± 1 , ± 1 2 , ± , 1 6 ± , 1 3 , ± 2 3 , ± 2, ± 3 and ± 6 Now, apply synthetic devisor method for x = 1 2 . 1 2 18 − 9 − 8 4 9 0 − 4 18 0 − 8 0 The factor of polynomial 18 x 3 − 9 x 2 − 8 x + 4 are ( x − 1 2 ) ( 18 x 2 − 8 ) . Consider the quadratic equation, 18 x 2 − 8 Factor the quadratic equation 18 x 2 − 8 , ( 18 x 2 − 8 ) = 18 x 2 − 8 = 2 ( 9 x 2 − 4 ) = 2 ( 3 x + 2 ) ( 3 x − 2 ) The factor of polynomial 18 x 3 − 9 x 2 − 8 x + 4 are 2 ( x − 1 2 ) ( 3 x + 2 ) ( 3 x − 2 ) . To find zeros set first term of the factor 2 ( x − 1 2 ) ( 3 x + 2 ) ( 3 x − 2 ) equal to zero. ( x − 1 2 ) = 0 x = 1 2 To find zeros set second term factor 2 ( x − 1 2 ) ( 3 x + 2 ) ( 3 x − 2 ) equal to zero

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Chapter A4, Problem 74E

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Chapter A4, Problem 73E

Chapter A4, Problem 75E

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Chapter A4 Solutions

CALCULUS: APPLIED APPROACH LOW COST MA

Ch. A4 - Prob. 1CP Ch. A4 - Prob. 2CP Ch. A4 - Prob. 3CP Ch. A4 - Prob. 4CP Ch. A4 - Prob. 1E Ch. A4 - Prob. 2E Ch. A4 - Prob. 3E Ch. A4 - Prob. 4E Ch. A4 - Prob. 5E Ch. A4 - Prob. 6E

Ch. A4 - Prob. 7E Ch. A4 - Prob. 8E Ch. A4 - Prob. 9E Ch. A4 - Prob. 10E Ch. A4 - Prob. 11E Ch. A4 - Prob. 12E Ch. A4 - Prob. 13E Ch. A4 - Prob. 14E Ch. A4 - Prob. 15E Ch. A4 - Prob. 16E Ch. A4 - Factoring Polynomials In Exercises 9-18, write the...Ch. A4 - Prob. 18E Ch. A4 - Prob. 19E Ch. A4 - Prob. 20E Ch. A4 - Prob. 21E Ch. A4 - Prob. 22E Ch. A4 - Prob. 23E Ch. A4 - Prob. 24E Ch. A4 - Prob. 25E Ch. A4 - Prob. 26E Ch. A4 - Prob. 27E Ch. A4 - Prob. 28E Ch. A4 - Prob. 29E Ch. A4 - Prob. 30E Ch. A4 - Prob. 31E Ch. A4 - Prob. 32E Ch. A4 - Prob. 33E Ch. A4 - Prob. 34E Ch. A4 - Prob. 35E Ch. A4 - Prob. 36E Ch. A4 - Prob. 37E Ch. A4 - Prob. 38E Ch. A4 - Prob. 39E Ch. A4 - Prob. 40E Ch. A4 - Prob. 41E Ch. A4 - Prob. 42E Ch. A4 - Prob. 43E Ch. A4 - Prob. 44E Ch. A4 - Prob. 45E Ch. A4 - Prob. 46E Ch. A4 - Prob. 47E Ch. A4 - Prob. 48E Ch. A4 - Prob. 49E Ch. A4 - Prob. 50E Ch. A4 - Prob. 51E Ch. A4 - Prob. 52E Ch. A4 - Prob. 53E Ch. A4 - Prob. 54E Ch. A4 - Prob. 55E Ch. A4 - Prob. 56E Ch. A4 - Prob. 57E Ch. A4 - Prob. 58E Ch. A4 - Prob. 59E Ch. A4 - Prob. 60E Ch. A4 - Prob. 61E Ch. A4 - Prob. 62E Ch. A4 - Prob. 63E Ch. A4 - Prob. 64E Ch. A4 - Prob. 65E Ch. A4 - Prob. 66E Ch. A4 - Prob. 67E Ch. A4 - Prob. 68E Ch. A4 - Prob. 69E Ch. A4 - Prob. 70E Ch. A4 - Prob. 71E Ch. A4 - Prob. 72E Ch. A4 - Prob. 73E Ch. A4 - Prob. 74E Ch. A4 - Prob. 75E Ch. A4 - Prob. 76E

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The factor the polynomial 18 x 3 − 9 x 2 − 8 x + 4 .

Solution Summary: The author explains how to calculate the factor of the polynomial 18x392-8x+4.

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To calculate: The factor the polynomial 18x3−9x2−8x+4.

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Chapter A4 Solutions