Explanation Given information: The provided expression is 2 z 3 − 2 z 2 − 24 z . Formula used: For factorizing a trinomial following steps have been followed: Step 1 : The polynomials of the trinomial are arranged in decreasing order. Step 2 : For evaluating the factor of constant term and coefficient of first-degree of the trinomial trial -and- error process is applied. Step 3 : If the constant term is positive, then the signs of the factors are of same sign as the sign of coefficient of first degree. Step 4 : If constant term is negative then one factor is positive and other is negative, if the sum of the factor is opposite of coefficient of first degree of a trinomial, changing the sign of each factor will give the required factorization. Step 5 : Verify by multiplying the evaluated binomial. FOIL method state that the by multiplication of two binomial ( p + a ) and ( p + b ) the provided trinomial is ( p + a ) ( p + b ) = p 2 + ( b + a ) p + a b Calculation: Consider the trinomial expression 2 z 3 − 2 z 2 − 24 z , The common factor 2 z is evaluated from the trinomial expression 2 z 3 − 2 z 2 − 24 z as follows, 2 z 3 − 2 z 2 − 24 z = 2 z ( z 2 − z − 12 ) Now consider the trinomial z 2 − z − 12 in which the constant term is negative. Therefore one factor of the provided trinomial must be positive and another one is negative. The coefficient of first degree in the provided trinomial z 2 − z − 12 is − 1 so consider the two factors of − 12 by trial-error-process such that their sum must be − 1

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ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 11.2, Problem 37ES

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Chapter 11.2, Problem 36ES

Chapter 11.2, Problem 38ES

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The factorization of trinomial expression 2 z 3 − 2 z 2 − 24 z .

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