Mathematics
Find the value of a, if the division of ax3 + 9x2 + 4x - 10 by x + 3 leaves a remainder 5.
Factorisation
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Answer
x + 3 = 0 ⇒ x = -3.
Given, when ax3 + 9x2 + 4x - 10 is divided by x + 3, the remainder is 5.
∴ On substituting x = -3 in ax3 + 9x2 + 4x - 10, remainder = 5.
⇒ a(-3)3 + 9(-3)2 + 4(-3) - 10 = 5
⇒ -27a + 81 - 12 - 10 = 5
⇒ -27a + 59 = 5
⇒ 27a = 59 - 5
⇒ 27a = 54
⇒ a = = 2
Hence, a = 2.
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