Question

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

Answer 1

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.

Answer 2

$\boxed {\underline {\mathbb {CORRECT \: QUESTION:-}}}$

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

$\boxed {\underline {\mathbb {GIVEN:-}}}$

(x+5)

polynomial F(x) = x³+x²+3x+115​

$\boxed {\underline {\mathbb {TO\:PROVE:-}}}$

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

$\boxed {\underline {\mathbb {THINGS\:TO\:ASSUME:-}}}$

$x=-5$

$\boxed {\underline {\mathbb {SOLUTION:-}}}$

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

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

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

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

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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