Question

find the remainder when x100 is divided by x2-3x+2

Answer 1

Given Equations :

• x² - 3x + 2 & x¹⁰⁰

To Find :

• The remainder when both the polynomials are divided.

Have a look at the attachment!

____________

When we divide x¹⁰⁰ with x² - 3x + 2,

⟶ The remainder we get is 3x⁵¹ + 2x⁵⁰

⟶ The Quotient is x⁵⁰

_________________

$\sf{VerificatioN}$

We know that, a = bq + r.

Where,

• a = Divident
• b = Divisor
• q = Quotient
• r = remainder

So now,

⟶ x¹⁰⁰ = ( x² - 3x + 2 ) × ( x⁵⁰ ) + ( 3x⁵¹ + 2x⁵⁰ )

⟶ x¹⁰⁰ = ( x¹⁰⁰ - 3x⁵¹ + 2x⁵⁰ ) + ( 3x⁵¹ + 2x⁵⁰ )

⟶ x¹⁰⁰ = x¹⁰⁰

$\boxed{\sf{Hence\:Verified!}}$