Multiply the polynomials (x-1)(x* +x³ +down an identity for (x - 1)(x" +x"-1 +..+x² +x + 1) for n a positive integer.+x+1) using a table. Generalize the pattern that emerges by

Multiply the given polynomials using table (x-1)(x4+x3+x2+x+1) x4 x3 x2 x 1 x x5 x4 x3 x2 x…

Answered: Multiply the polynomials (x-1)(x* +x³ +…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter8: Polynomials

Section8.1: Adding And Subtracting Polynomials

Problem 63HP

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Multiply the polynomials (x-1)(x* +x³ +
down an identity for (x - 1)(x" +x"-1 +..+x² +x + 1) for n a positive integer.
+x+1) using a table. Generalize the pattern that emerges by

Expert Solution

Step 1

Multiply the given polynomials using table

$(x - 1) (x^{4} + x^{3} + x^{2} + x + 1)$

	$x^{4}$	$x^{3}$	$x^{2}$	x	1
x	$x^{5}$	$x^{4}$	$x^{3}$	$x^{2}$	x
-1	$- x^{4}$	$- x^{3}$	$- x^{2}$	-x	-1

Now we add all the terms that we multiplied in the table

$x^{5} + x^{4} + x^{3} + x^{2} + x - x^{4} - x^{3} - x^{2} - x - 1 C o m b i n e l i k e t e r m s x^{5} + x^{4} - x^{4} + x^{3} - x^{3} + x^{2} - x^{2} + x - x - 1 x^{5} - 1$

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