Question

Q14 Using Remainder Theorem, find the remainder when 3 4 12 4 2 x − x + x − is divided by x − 3

Answer 1

SOLUTION

TO DETERMINE

Use the Remainder Theorem, find the remainder when

$\sf{ {x}^{4} - 3 {x}^{2} + 4x - 12}$

is divided by x - 3

EVALUATION

Let

f(x) = x - 3

$\sf{ g(x) = {x}^{4} - 3 {x}^{2} + 4x - 12}$

For Zero of the polynomial f(x) we have

f(x) = 0

⇒ x - 3 = 0

⇒ x = 3

Noe by the Remainder Theorem the required Remainder when g(x) is divided by f(x) is

$\sf{ = g(3)}$

$\sf{ = {(3)}^{4} - 3 \times {(3)}^{2} + 4 \times 3 - 12}$

$\sf{ =81 - 27 + 12 - 12 }$

$\sf{ =54}$

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