Check whether p(x) is a multiple of g(x) or not p(x)=x^3-5x^2+4x-3, g(x)=x-2

daniko883y 2022-09-04 Answered
Check whether p(x) is a multiple of g(x) or not
p ( x ) = x 3 5 x 2 + 4 x 3
g ( x ) = x 2
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Answers (2)

Elisa Spears
Answered 2022-09-05 Author has 9 answers
MathJax(?): Can't find handler for document MathJax(?): Can't find handler for document Step 1
Given
p ( x ) = x 3 5 x 2 + 4 x 3
g ( x ) = x 2Step 2 Finding the given
According to the question,
= g ( x ) = x 2
g ( x ) = 0
x 2 = 0
x = 2
zero of g ( x ) = 2
So, substituning the value of x in p(x).
p ( 2 ) = ( 2 ) 3 5 ( 2 ) 2 + 4 ( 2 ) 3
p ( 2 ) = ( 2 ) 3 5 ( 2 ) 2 + 4 ( 2 ) 3
= 7 0
\therefore p(x) is not the multiple of g(x) since the remainder 0
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Inbrunstlr
Answered 2022-09-06 Author has 2 answers
Given, p ( x ) = x 3 5 x 2 + 4 x 3
g ( x ) = x 2
x 2 = 0
x = 2
Now, p(2) should be 0 if p(x) is a multiple of g(x)
Thus,
p ( 2 ) = 2 3 5 ( 2 ) 2 + 4 ( 2 ) 3
= 8 20 + 8 3
= 7
= 8 20 + 8 3
= 0
Thus, p(x) is not a multiple of g(x)
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