find the remainder when x cube + 3 X square + 3 X + 1 divided by X + 22/7
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Step-by-step explanation:
We use the Remainder theorem which states that if a polynomial p(x) is divided with a linear polynomial x - a then the remainder is given by p(a).
Here p(x) = x³ + 3x² + 3x + 1
and linear polynomial = x+\pix+π
now according to remainder theorem,
remainder=p(-\pi)remainder=p(−π)
=(-\pi)^3+3(-\pi)^2+3(-\pi)+1=(−π)
3
+3(−π)
2
+3(−π)+1
=-\pi^3+3\pi^2-3\pi+1=−π
3
+3π
2
−3π+1
we further solve it by putting value of \piπ .i.e, \pi=\frac{22}{7}π=
7
22
remainder=-(\frac{22}{7})^3+3(\frac{22}{7})^2-3(\frac{22}{7})+1remainder=−(
7
22
)
3
+3(
7
22
)
2
−3(
7
22
)+1
remainder=-9.84remainder=−9.84
Therefore, Remainder = -9.84
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