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Long Division Method to Divide Two Polynomials

Use remainder...

Question

Use remainder theorem to find the value of $k$ , it being given that when $x^{3} + 2 x^{2} + k x + 3$ is divided by $(x - 3)$ , then the remainder is $21$ .

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Solution

$x^{3} + 2 x^{2} + k x + 3 ∴ f (3) = 21 3^{3} + 2. 3^{2} - 3 k - 3 = 21 9 + 6 + k + 1 = 7 k = - 9$

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