(b) 7 is the correct answer.
see the attachment below for solution.
Answer:
7
Step-by-step explanation:
[tex] \huge\mathfrak{\green{solution}}[/tex]
Given polynomial is,
[tex]1 +x + + {x}^{3} + {x}^{9} + {x}^{27} + {x}^{81} + {x}^{243} \\ [/tex]
Here we have to find the remainder when this polynomial is divided by x - 1.
Let us assume that,
[tex]f(x) = 1 +x + {x}^{3} + {x}^{9} + {x}^{27} + {x}^{81} + {x}^{243} \\ [/tex]
Next we have to equate x - 1 = 0.
So,
[tex]x - 1 = 0[/tex]
[tex]\dashrightarrow \: x = 0 + 1[/tex]
[tex]\dashrightarrow \: x = 1[/tex]
Next,
[tex]f( 1) = 1 +1 + {1}^{3} + {1}^{9} + {1}^{27} + {1}^{81} + {1}^{243} \\ [/tex]
[tex]\dashrightarrow \: 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 \\ [/tex]
[tex]\dashrightarrow \: 7[/tex]
Therefore 7 is the remainder when the given polynomial is divided by x - 1.
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Answer :-
(b) 7 is the correct answer.
see the attachment below for solution.
Answer:
7
Step-by-step explanation:
[tex] \huge\mathfrak{\green{solution}}[/tex]
Given polynomial is,
[tex]1 +x + + {x}^{3} + {x}^{9} + {x}^{27} + {x}^{81} + {x}^{243} \\ [/tex]
Here we have to find the remainder when this polynomial is divided by x - 1.
Let us assume that,
[tex]f(x) = 1 +x + {x}^{3} + {x}^{9} + {x}^{27} + {x}^{81} + {x}^{243} \\ [/tex]
Next we have to equate x - 1 = 0.
So,
[tex]x - 1 = 0[/tex]
[tex]\dashrightarrow \: x = 0 + 1[/tex]
[tex]\dashrightarrow \: x = 1[/tex]
Next,
[tex]f( 1) = 1 +1 + {1}^{3} + {1}^{9} + {1}^{27} + {1}^{81} + {1}^{243} \\ [/tex]
[tex]\dashrightarrow \: 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 \\ [/tex]
[tex]\dashrightarrow \: 7[/tex]
Therefore 7 is the remainder when the given polynomial is divided by x - 1.