Find all zeros of the polynomial P(x)=x^5 +x^3 +8x^2 +8

driliwra7

driliwra7

Answered question

2022-09-04

Find all zeros of the polynomial
P ( x ) = x 5 + x 3 + 8 x 2 + 8

Answer & Explanation

Cristian Delacruz

Cristian Delacruz

Beginner2022-09-05Added 13 answers

factor and then set to 0 and solve
To factor by grouping
x 5 + x 3 + 8 x 2 + 8 group 2 terms together
( x 5 + x 3 ) + ( 8 x 2 + 8 ) factor each grouping
x 3 ( x 2 + 1 ) + 8 ( x 2 + 1 ) combine
( x 3 + 8 ) ( x 2 + 1 ) = 0 set each factor to 0
( x 3 + 8 ) = 0 x 2 + 1 = 0 solve for x
x 3 = 8 x 2 = 1
x = 2 , x = 1
curukksm

curukksm

Beginner2022-09-06Added 2 answers

P ( x ) = x 5 + x 3 + 8 x 2 + 8
P ( x ) = ( x 5 + x 3 ) + ( 8 x 2 + 8 )
P ( x ) = x 3 ( x 2 + 1 ) + 8 ( x 2 + 1 )
P ( x ) = ( x 3 + 8 ) ( x 2 + 1 ) = 0
x = 2

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