(x - 2) is a factor of the expression x³ + ax² + bx + 6. When this expression is divided by (x - 3), it leaves the remainder 3. Find the values of a and b.
Factorisation
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Question

(x - 2) is a factor of the expression x³ + ax² + bx + 6. When this expression is divided by (x - 3), it leaves the remainder 3. Find the values of a and b.

KnowledgeBoat · Accepted Answer

Let f(x) = x³ + ax² + bx + 6 Given, (x - 2) is factor of f(x), hence, f(2) = 0 by factor's theorem Given, on dividing f(x) by (x - 3) remainder left is 3 By remainder theorem, remainder = f(3) On dividing equation by 3, Putting value of b from equation 1, Hence, the value of a = -3 and b = -1.

Mathematics

(x - 2) is a factor of the expression x³ + ax² + bx + 6. When this expression is divided by (x - 3), it leaves the remainder 3. Find the values of a and b.

Factorisation

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