Let f(x) and g (x) be two non-zero polynomials in R[x], R being any ring. (i) If f (x) + g (x) # 0, then deg (f (x) + g (x))

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Let f(x) and g (x) be two non-zero polynomials in<br>R[x], R being any ring.<br>(i) If f (x) + g (x) # 0, then<br>deg (f (x) + g (x)) < max (degf (x), deg g (x)).<br>(ii) If f (x) g (x) # 0, then deg (f (x) g (x)) < degf (x) + deg g (x).<br>(iii) If R is an integral domain, then<br>deg (f (x) g (x)) = deg f (x) + deg g (x).<br>%3D<br>

Extracted text: Let f(x) and g (x) be two non-zero polynomials in R[x], R being any ring. (i) If f (x) + g (x) # 0, then deg (f (x) + g (x)) < max="" (degf="" (x),="" deg="" g="" (x)).="" (ii)="" if="" f="" (x)="" g="" (x)="" #="" 0,="" then="" deg="" (f="" (x)="" g="" (x))="">< degf="" (x)="" +="" deg="" g="" (x).="" (iii)="" if="" r="" is="" an="" integral="" domain,="" then="" deg="" (f="" (x)="" g="" (x))="deg" f="" (x)="" +="" deg="" g="" (x).="">

Jun 04, 2022

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Let f(x) and g (x) be two non-zero polynomials in R[x], R being any ring. (i) If f (x) + g (x) # 0, then deg (f (x) + g (x))

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