find the reminder when x²+3x²+3x+1 is divided by
________
1) x+1
2)x-¹/2
3)x
4(x+π
5)5+2x
_____RULES...
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Answers
Answer:
(i) = 0
(ii) = 27/8
(iii) = 1
(iv) = -\pi ^3+3\pi ^2-3\pi +1−π
3
+3π
2
−3π+1
(v) = -27/8
Step-by-step explanation:
\begin{gathered}(i)x+1=0\\x=-1\\\end{gathered}
(i)x+1=0
x=−1
put x = -1 in equation (i)
\begin{gathered}(-1)^3+3\times(-1)^2+3\times(-1)+1\\-1+3-3+1\\=0\end{gathered}
(−1)
3
+3×(−1)
2
+3×(−1)+1
−1+3−3+1
=0
\begin{gathered}(ii)x-\frac{1}{2}=0\\x=\frac{1}{2}\\\end{gathered}
(ii)x−
2
1
=0
x=
2
1
put x=1/2 in equation (i)
\begin{gathered}(\frac{1}{2}) ^3+3\times(\frac{1}{2})^2+3\times(\frac{1}{2})+1\\\frac{1}{8}+3\times\frac{1}{4}+\frac{3}{2}+1\\\frac{1}{8}+\frac{3}{4}+\frac{3}{2}+\frac{1}{1}\\\frac{1+6+12+8}{8}=\frac{27}{8}\end{gathered}
(
2
1
)
3
+3×(
2
1
)
2
+3×(
2
1
)+1
8
1
+3×
4
1
+
2
3
+1
8
1
+
4
3
+
2
3
+
1
1
8
1+6+12+8
=
8
27
\begin{gathered}(iii)x=0\\\end{gathered}
(iii)x=0
put x=0 in equation (i)
\begin{gathered}0^3+3\times0^2+3\times0+1\\0+0+0+1\\=1\end{gathered}
0
3
+3×0
2
+3×0+1
0+0+0+1
=1
\begin{gathered}(iv)x+\pi =0\\x=-\pi\end{gathered}
(iv)x+π=0
x=−π
put x=-\pix=−π in equation (i)
\begin{gathered}(-\pi)^3+3\times(-\pi)^2+3\times(-\pi)+1\\-\pi^3+3\pi^2-3\pi+1\\\end{gathered}
(−π)
3
+3×(−π)
2
+3×(−π)+1
−π
3
+3π
2
−3π+1
\begin{gathered}(v)5+2x=0\\2x=-5\\x=\frac{-5}{2}\\\end{gathered}
(v)5+2x=0
2x=−5
x=
2
−5
put x=\frac{-5}{2}x=
2
−5
in equation-(i)
\begin{gathered}(\frac{-5}{2})^33\times(\frac{-5}{2})^2+3(\frac{-5}{2})+1\\=\frac{-27}{8}\end{gathered}
(
2
−5
)
3
3×(
2
−5
)
2
+3(
2
−5
)+1
=
8
−27