# Show that 4x2+6x+3 is a unit in Z8[x].All that I know that I have to do is find a polynomial such that(4x2+6x+3)(polynomial)=1, but I'm not sure the steps in general to follow. I think after multiplying the two polynomials the coefficients will have to turn out to be 0 mod 8 and the constant term will have to be 1 mod 8.  How do I approach any problem of this type?  I have no examples to go by, and I need to know the thinking process that is needed to solve these types of problems.  Thanks!

Question

Show that 4x2+6x+3 is a unit in Z8[x].

All that I know that I have to do is find a polynomial such that

(4x2+6x+3)(polynomial)=1, but I'm not sure the steps in general to follow. I think after multiplying the two polynomials the coefficients will have to turn out to be 0 mod 8 and the constant term will have to be 1 mod 8.  How do I approach any problem of this type?  I have no examples to go by, and I need to know the thinking process that is needed to solve these types of problems.  Thanks!

check_circle

Step 1

Given polynomial is,

Step 2

Consider a polynomial as,

Step 3

Then the product of both t... help_outlineImage Transcriptionclose(4x 6x3(2.x+ 3) = 8x2 +12x2 +12x2 +18x +6x +9 = 8.x3 +24.x2 + 24x +9 fullscreen

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