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# If (X + 2) and (X + 3) Are Factors of X3 + Ax + B, Find the Values of 'A' and B'. - Mathematics

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#### Question

If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of 'a' and b'.

#### Solution

Given (x + 2) is a factor of x^3 + ax + b

=> (-2)^3 + a(-a) + b = 0   (x + 2 = 0 ⇒ x = -2)

=> -8-2a + b = 0

=> -2a + b = 8 .....(1)

Also,given that (x+ 3) is a factor of x3 + ax + b

=> (-3)^3 + a(-3) + b = 0

=> -27 - 3a + b = 0

=> -3a + b = 27  ...(2)

Subtracting (1) from (2) we have

-a = 19 => a = -19

Substituting a = -19 in (1), we have

-2 xx (-19) + b = 8

=> 38 + b = 8

=> b = -30

Hence, a = -19 and b = -30

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Solution If (X + 2) and (X + 3) Are Factors of X3 + Ax + B, Find the Values of 'A' and B'. Concept: Factor Theorem.
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