Explanation Given Information: The provided expression is x 4 − 20 x 3 − 100 x 2 . 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 the 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 the same sign as the sign of the coefficient of the first degree. Step 4 : If the 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. Calculation: Consider the trinomial expression x 4 − 20 x 3 − 100 x 2 . The common factor x 2 is evaluated from the trinomial expression x 4 − 20 x 3 − 100 x 2 as follows, x 4 − 21 x 3 − 100 x 2 = x 2 ( x 2 − 21 x − 100 ) Now consider the trinomial x 2 − 21 x − 100 in which the constant term is negative. Therefore both the factors of the provided trinomial must be of opposite sign. The coefficient of first degree in the provided trinomial x 2 − 21 x − 100 is − 21 . So, consider the two factors of − 100 by trial-error-process such that their sum must be − 21 . The all possible pairs of factors of − 100 in which the negative factor has larger absolute value are as follows, Pairs of possible factors of − 100 Sum of factors − 100 , + 1 − 99 − 50 , + 2 − 48 − 25 , + 4 − 21 − 10 , + 10 0 From trial-error-process coefficient of first degree of the provided trinomial x 2 − 21 x − 100 is equal to the sum of the factors of − 25 and + 4 which is − 21

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ISBN: 9781323235911

Author: BITTINGER

Publisher: Pearson Custom Publishing

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Chapter 11.2, Problem 41ES

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To calculate: The factorization of trinomial expression x4−20x3−100x2.

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Chapter 11.2, Problem 40ES

Chapter 11.2, Problem 42ES

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The factorization of trinomial expression x 4 − 20 x 3 − 100 x 2 .

Solution Summary: The author calculates the factorization of a trinomial expression using the following steps.

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