Madhya Pradesh Police Exam Model Paper 1

Question : 83 of 100

Marks: +1, -0

On dividing

–x^3 + 3x^2 – 3x + 5

by a polynomial f(x), the quotient and remainder are (x – 2) and 3, respectively, then, f(x) is –

$x^2 + x + 1$
$-x^2 + x +1$
$-x^2 + x – 1$
$–x^2 – x – 1$

Validate

Solution:

Given:
Dividend

= –x^3 + 3x^2 – 3x + 5

Divisor = f(x) =?
Quotient = (x – 2)
Remainder = 3
Concept used:
Dividend = Divisor × Quotient + Remainder
Calculation:
Dividend = Divisor × Quotient + Remainder

⇒ -x^3 + 3x^2 – 3x + 5 = f(x) × (x – 2) + 3

⇒ -x^3 + 3x^2 – 3x + 2 = f(x) × (x – 2)

⇒ f(x) = (- x^3 + 3x^2 – 3x + 2){/}(x – 2)

∴ f(x) = (-x^2 + x – 1)

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