Find a if the two polynomials ax^3 + 3x^2 − 9 and 2x^3 + 4x + a leave the same remainder when divided by (x + 3)

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By remainder theorem, If f(x) is divided by (x - a), then remainder = f(a). Let p(x) = ax3 + 3x2 - 9 and q(x) = 2x3 + 4x + a Given, Divisor : ⇒ x + 3 = 0 ⇒ x = -3 On dividing ax3 + 3x2 - 9 by x + 3, we get : ⇒ p(-3) = a(-3)3 + 3(-3)2 - 9 = -27a + 27 - 9 = -27a + 18. On dividing 2x3 + 4x + a by x + 3, we get : ⇒ q(-3) = 2(-3)3 + 4(-3) + a = -54 - 12 + a = -66 + a. Given, Polynomials ax3 + 3x2 - 9 and 2x3 + 4x + a leave the same remainder when divided by (x + 3). p(-3) = q(-3) ⇒ -27a + 18 = -66 + a ⇒ -27a - a = -66 - 18 ⇒ -28a = -84 ⇒ a = ⇒ a = 3. Hence, the value of a = 3.

Mathematics

Find a if the two polynomials ax³ + 3x² - 9 and 2x³ + 4x + a leave the same remainder when divided by (x + 3).

Factorisation

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Mathematics

Find a if the two polynomials ax3 + 3x2 - 9 and 2x3 + 4x + a leave the same remainder when divided by (x + 3).

Factorisation

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