Factor each of the following polynomials as the product of two polynomials of degree 1 in Z_{10}[x]. x+9

Cheyanne Leigh

Cheyanne Leigh

Answered question

2021-09-07

Factor each of the following polynomials as the product of two polynomials of degree 1 in Z10[x].
x+9

Answer & Explanation

Maciej Morrow

Maciej Morrow

Skilled2021-09-08Added 98 answers

To factor the polynomial x+9 as the product of two polynomials of degree in Z10[x]
Consider two polynomials (5x+3) and (2x+3) of degree 1 in Z10[x]
The product of the two polynomials is given as,
(5x+3)(2x+3)=(5×2)x2+(5×3)x+(3×2)x+9
=10x2+15x+6x+9
=0.x2+(15+6)x+9
=0.x2+21x+9
=x+9
since 10=0,21=1 in Z10[x]
Therefore, x+9 is dactored as a product of two polynomials (5x+3) and (2x+3) of degree 1 in Z10[x].

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