Question

When the polynomial P(x) = x3

+ 3x2

– 2Ax + 3,

where A is constant, is divided by x2

+ 1 and

remainder is –5x, then A is

Answer 1

the value of A = 2.

Answer 2

Answer:

Value of A is 2

Step-by-step explanation:

Given the polynomial

$P(x)=x^3+3x^2-2Ax+3$

is divided by $x^2+1$ and remainder is -5x then

we have to find the value of A

By Euclid algorithm

$Dividend=Divisor\times quotient +Remainder$

$x^3+3x^2-2Ax+3=(x^2+1)\times (ax+b)-5x$

$x^3+3x^2-2Ax+3=ax^3 + bx^2 + ax + b - 5x$

$x^3 + 3x^2 - 2Ax + 3=ax^3 + bx^2 + (a - 5)x + b$

Compare each term:

a = 1, b = 3

a - 5 = -2A

1-5 = -2A => A = 2

Hence, value of A is 2