Find the remainder when x3 + 3x2 + 3x + 1 is divided by the following Linear polynomials:
x + π
Let p(x) = x3 + 3x2 + 3x + 1
As we know by Remainder Theorem,
If a polynomial p(x) is divided by a linear polynomial (x – a) then, the remainder is p(a)
⇒ Remainder of p(x) when divided by x + π is p(–π)
p(–π) = (–π)3+ 3(–π)2+ 3(–π) + 1
⇒ p(–π)= –π3 + 3π2 –3π + 1
∴ Remainder of x3 + 3x2 + 3x + 1 when divided by x+ π is –π3 + 3π2 –3π + 1
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