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

1.	Find the remainder when x100 is divided by x2-3x+2
Answer» 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 $\boxed{\sf{Hence\:Verified!}}$

Answer»

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,

So now,

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

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

⟶ x¹⁰⁰ = x¹⁰⁰

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

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