Determine the binomial factors of x^3+3x^2+3x+1.

Clinton Mccormick

Clinton Mccormick

Answered question

2023-02-16

Determine the binomial factors of x 3 + 3 x 2 + 3 x + 1

Answer & Explanation

Izaiah Bean

Izaiah Bean

Beginner2023-02-17Added 6 answers

( - 1 ) 3 + 3 ( - 1 ) 2 + 3 ( - 1 ) + 1 = - 1 + 3 - 3 + 1 = 0 , so its root at x=-1
( 1 ) 3 + 3 ( 1 ) 2 + 3 ( 1 ) + 1 = 1 + 3 + 3 + 1 = 8 , so not a root at x=1
( x - root ) = ( x - ( - 1 ) ) = ( x + 1 ) - factors of the polynomial
Divide the polynomial by (x+1) - x 3 + 3 x 2 + 3 x + 1 x + 1 = x 3 + x 2 + x 2 + x + x 2 + x + x + 1 x + 1
= ( x 3 + x 2 ) + ( x 2 + x ) + ( x 2 + x ) + ( x + 1 ) x + 1
= ( x 2 + x + x + 1 )
= x 2 + 2 x + 1
( x + 1 ) ( x + 1 ) 2 = ( x + 1 ) 3

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