Answer:
Remainder=292
Step-by-step explanation:
x+3=0
x=-3
p(-3)=(-3)^4-9(-3)^3-5(-3)^2-3(-3)+4
=81+243-45+9+4
=337-45
=292
The required remainder is [tex]292[/tex].
Given:
The given polynomial is [tex]P(x)=x^4-9x^3-5x^2-3x+4[/tex].
[tex]P(x)[/tex] is divided by [tex]x+3[/tex].
To find:
The remainder by using the Remainder Theorem.
Explanation:
According to the Remainder Theorem, if a polynomial [tex]P(x)[/tex] is divided by [tex](x-c)[/tex], then the remainder is [tex]P(c)[/tex].
It is given that [tex]P(x)[/tex] is divided by [tex]x+3[/tex]. By using the Remainder Theorem, the remainder is [tex]P(-3)[/tex].
[tex]P(-3)=(-3)^4-9(-3)^3-5(-3)^2-3(-3)+4[/tex]
[tex]P(-3)=81-9(-27)-5(9)+9+4[/tex]
[tex]P(-3)=81+243-45+13[/tex]
[tex]P(-3)=292[/tex]
Therefore, the required remainder is [tex]292[/tex].
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