Sol.

On dividing x³ – 3x² + x + 2 by a polynomial g(x), the quotient

and remainder were x – 2 and – 2x + 4, respectively. Find g(x).

Dividend

= Divisor

× Quotient

+ Remainder

x³ – 3x² + x + 2

=

g(x)

×

(x – 2)

+

(–2x + 4)

∴

g(x)

×

(x – 2)

=

x³ – 3x² + x + 2

+ 2x – 4

∴

g(x)

(x – 2)

=

x³ – 3x² + x + 2

+ 2x – 4

∴

g(x)

=

x³

– 3x²

+ 3x

– 2

(x – 2)

x³ – 3x² + x + 2

=

g(x)

×

(x – 2)

– 2x + 4

∴

+ 2

+ 2x

+ x

– 4

Sol.

On dividing x³ – 3x² + x + 2 by a polynomial g(x), the quotient

and remainder were x – 2 and – 2x + 4, respectively. Find g(x).

Dividend

= Divisor

× Quotient

+ Remainder

x³

x

=

x³

–

2x²

x²

=

–x²

x

=

– x²

+

2x

–x

=

x – 2

x³ – 3x² + 3x – 2

(–)

x³ – 2x²

(+)

+ 3x

–

– 2

– x

– x² + 2x

(–)

– 2

(+)

x

– x²

+

x²

x²

(x – 2)

– x

(x – 2)

–

–

²

x

x

=

x

–

2

1

=

1

(x – 2)

x – 2

(–)

(+)

0

+ 1

Quotient =

∴

Remainder =

x² – x + 1

0

Dividend should

be in index form