Question

when x cube + 2 X square + 4 x + b is divided by X + 1 the quotient is X square + aX + 3 and reminder is - 3 + 2 b find the values of a and b​

Answer 1

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Answer 2

Therefore a = 1 and b = 3

Step-by-step explanation:

We know that

Polynomial = Divisor × Quotient +Remainder

$x^3 +2x^2+4x +b =(x^2+ax+3)(x+1) + (-3+2b)$

$x^3 +2x^2+4x +b =(x^2+ax+3 +x^3+ax^2+3x) + (-3+2b)$

$x^3 +2x^2+4x +b =x^3 +(a+1)x^2+(a+3)x+(-3+2b)$

Equating the coefficient of $x^{2}$ and constant term

a+1=2                      and                         -3+2b = b

⇔ a = 1                                                  ⇔b=3