Question

Find the remainder when
x3+3x2+3x+1 is divided by x - 1​

Answer 1

REMAINDER THEOREM:

When a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x equal to k, the remainder is given by r=a(k).

Formula is: p(x) = (x-c)·q(x) + r(x).

SO, BY remainder theorem

x+1=0

x=−1

p(x)=x  ^3  +3x^ 2  −3x^−1p(−1)

=(−1)  

3 +3(−1)  ^2 −3(−1)^−1

=−1+3(1)+3−1

=−1+3+3−1

=6−2

=4

Thus remainder is 4

Answer 2

➸ Given:-

• f(x) = x³+3x²+3x+1
• g(x) = x-1

☣ To Find:-

• Remainder.

☢ Solution:-

$g(x) = x - 1 \\ x - 1 = 0 \\ x = 1$

By Substituting the Value of x in f(x).

${x}^{3} + 3 {x}^{2} + 3x + 1 \\ {1}^{3} + 3( {1})^{2} + 3(1) + 1 \\ 1 + 3 + 3 + 1 \\ 8$

• The Remainder ☞ $\Large\red{\bold{8}}$

Quotient:- x²+4x+7

$\boxed{\tt{@MrMonarque}}$

Hope It Helps You ✌️