Question

find the remainder and quotient when x^3 +3x^2+3x+1 dividend by x+1​

Answer 1

Question :- find the remainder and quotient when x^3 +3x^2+3x+1 dividend by x+1 ?

Answer :-

Dividing by long divison method we get,

x + 1 ) x³ +3x² + 3x + 1 (x² + 2x + 1

x³ + x²

2x² + 3x

2x² + 2x

x + 1

x + 1

0

therefore, we get,

→ Quotient = (x² + 2x + 1)

→ Remainder = 0

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Answer 2

$\underline{\textbf{Given:}}$

$\textsf{PolynomiaL is}$

$\mathsf{x^3+3x^2+3x+1}$

$\underline{\textbf{To find:}}$

$\textsf{The remainder and quotient when}$

$\mathsf{x^3+3x^2+3x+1\;is\;divided\;by\;(x+1)}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{x^3+3x^2+3x+1}$

$\textsf{This can be written as}$

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

$\mathsf{=x(x^2+2x+1)+1(x^2+2x+1)}$

$\mathsf{=(x+1)(x^2+2x+1)}$

$\implies\mathsf{x^3+3x^2+3x+1=(x+1)(x^2+2x+1)}$

$\implies\mathsf{(x+1)\;exactly\;divides\;x^3+3x^2+3x+1}$

$\therefore\underline{\mathsf{The\;reminder\;when\;x^3+3x^2+3x+1\;is\;divided\;by\;x+1\;is\;0}}$

$\underline{\textbf{Find more:}}$

If 81x⁴-72x³+px²-8x+1 is a perfect square the find the value of p

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