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

daniko883y

Answered question

2022-09-04

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

Answer & Explanation

Elisa Spears

Elisa Spears

Beginner2022-09-05Added 9 answers

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

Inbrunstlr

Inbrunstlr

Beginner2022-09-06Added 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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