Show that (x-5) is a factor of the polynomial F(x) = x³+x²+3x+115​

2 thoughts on “Show that (x-5) is a factor of the polynomial F(x) = x³+x²+3x+115​”

1. [tex]\boxed {\underline {\mathbb {CORRECT \: QUESTION:-}}}[/tex]

   Show that (x+5) is a factor of the polynomial f(x)=x³+x²+3x+115

   [tex]\boxed {\underline {\mathbb {GIVEN:-}}}[/tex]

   (x+5)

   polynomial F(x) = x³+x²+3x+115​

   [tex]\boxed {\underline {\mathbb {TO\:PROVE:-}}}[/tex]

   (x+5) is a factor of the polynomial F(x) = x³+x²+3x+115​

   [tex]\boxed {\underline {\mathbb {THINGS\:TO\:ASSUME:-}}}[/tex]

   [tex]x=-5[/tex]

   [tex]\boxed {\underline {\mathbb {SOLUTION:-}}}[/tex]

   If (x+5) makes F(x)=0 than it implies that it is a factor of [tex]x^{3}+x^{2}+3x+115[/tex]
   Therefore x+5=0

   Hence [tex]\boxed{x=-5}[/tex] [brought 5 to R.H.S. thus getting x=-5]

   Now as we got x value of let’s put in [tex]F(5)=x^{3}+x^{2}+3x+115[/tex]

   [tex]=5^{3}+5^{2}+3(5)+115\\=(-5 \times -5 \times -5) + (-5 \times -5 )+(3 \times -5 )+115\\=-125+25-15+115\\=-125-15+25+115\\=-140+140\\\boxed{F(x)=0}[/tex]

   hence as f(x)=0 which means that (x+5) is a factor of the polynomial F(x) = x³+x²+3x+115​

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2. Answer:

   If (x+5) is a factor of f (x) then x+5=0:x=-5:should satisfy f (x)

   Source putting -5 in f (x)…

   (-5)³+(-5)²+3×(-5)+115

   =-125+25-15+115

   =0

   Hence proved.

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