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Division Algorithm for a Polynomial

Perform the d...

Question

Perform the division: $x^{3} - 5 x^{2} + 8 x - 4$ by $x - 2$

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Solution

Divide $x^{3} - 5 x^{2} + 8 x - 4$ by $x - 2$ as shown above:

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Q. Perform the division:

x^{3} - 1

x - 1

(x - 1)

is one of the factors of the polynomial

(x^{3} - 5 x^{2} + 8 x - 4),

then find the other factors using synthetic division.

x^{3} - 5 x^{2} + 7

is divisible by

(x + 2)

, then the remainder is

Find the factors of the expression $x^{3} - 5 x^{2} + 8 x - 4$

p (x) = 2 x^{4} - 3 x^{3} - 5 x^{2} + 8 x - 3

, find the remainder when

p (x)

(x - \frac{3}{2})

. Also, verify the result by actual division.

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