If (x + 2) and (x - 3) are the factors of x³ + ax + b, find the values of a and b. With these values of a and b, factorise the given expression.
Factorisation
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Question

If (x + 2) and (x - 3) are the factors of x³ + ax + b, find the values of a and b. With these values of a and b, factorise the given expression.

KnowledgeBoat · Accepted Answer

f(x) = x³ + ax + b If (x + 2) or (x - (-2)) and (x - 3) are factors of f(x) then, f(-2) and f(3) = 0. Putting value of b = 2a + 8 from equation 1, Putting the values of a and b in f(x) we get, f(x) = x³ - 7x - 6 Since, (x + 2) and (x - 3) are factors of f(x) hence, (x + 2)(x - 3) = (x² - x - 6) is also the factor. On dividing f(x) by x² - x - 6, we get, (x + 1) as quotient and remainder = 0. Hence, the value of a = -7 and b = -6; x³ - 7x - 6 = (x + 2)(x - 3)(x + 1).

Mathematics

If (x + 2) and (x - 3) are the factors of x³ + ax + b, find the values of a and b. With these values of a and b, factorise the given expression.

Factorisation

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