Explanation Given Information: The polynomial is 3 x 4 − 48 . Formula used: The factorization of a difference of square is, A 2 − B 2 = ( A + B ) ( A − B ) Calculation: Consider the provided polynomial 3 x 4 − 48 . The polynomial has 3 as the greatest common factor. Factor out the greatest common factor 3 from the polynomial 3 x 4 − 48 as follows: 3 x 4 − 48 = 3 ( x 4 − 16 ) The resultant polynomial x 4 − 16 has only two terms. Express the two terms as perfect squares: x 4 = ( x 2 ) 2 and 16 = ( 4 ) 2 As both the terms are perfect squares the polynomial x 4 − 16 can be factorized by difference of squares. Factor the expression x 4 − 16 using the difference of squares as follows: x 4 − 16 = ( x 2 + 4 ) ( x 2 − 4 ) Factorize the last polynomial x 2 − 4 further using the difference of squares as follows: Express the two terms as perfect squares: x 2 = ( x ) 2 and 4 = ( 2 ) 2 As both the terms are perfect squares the polynomial x 2 − 4 can be factorized by difference of squares. Factor the expression x 2 − 4 using the difference of squares as follows: x 2 − 4 = ( x + 2 ) ( x − 2 ) None of the resultant factors can be factorized further

9th Edition

ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 11, Problem 14T

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The factorization of the polynomial 3 x 4 − 48 .

Solution Summary: The author calculates the factorization of the polynomial 3x4-48 based on a difference of squares.

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To calculate: The factorization of the polynomial 3x4−48.

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