On dividing (ax^3 + 9x^2 + 4x − 10) by (x + 3), we get 5 as remainder. Find the value of a.

Question

KnowledgeBoat · Accepted Answer

By remainder theorem, If f(x) is divided by (x - a), then remainder = f(a). Let f(x) = ax3 + 9x2 + 4x - 10 Given, Remainder = 5 Divisor : ⇒ x + 3 = 0 ⇒ x = -3. Substituting x = -3 in f(x), will give remainder 5. ⇒ f(-3) = 5 ⇒ a(-3)3 + 9(-3)2 + 4(-3) - 10 = 5 ⇒ a(-27) + 81 - 12 - 10 = 5 ⇒ -27a + 81 - 22 = 5 ⇒ -27a + 59 = 5 ⇒ -27a = 5 - 59 ⇒ -27a = -54 ⇒ a = ⇒ a = 2. Hence, the value of a = 2.

Mathematics

On dividing (ax³ + 9x² + 4x - 10) by (x + 3), we get 5 as remainder. Find the value of a.

Factorisation

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Mathematics

On dividing (ax3 + 9x2 + 4x - 10) by (x + 3), we get 5 as remainder. Find the value of a.

Factorisation

Related Questions

Using remainder theorem, find the remainder when:f(x) = 9x2 - 6x + 2 is divided by (3x - 2).

Using remainder theorem, find the remainder when:f(x) = 8x2 - 2x - 15 is divided by (2x + 3).

Using Remainder Theorem, find the value of k if on dividing 2x3 + 3x2 - kx + 5 by (x - 2), leaves a remainder 7.

If the polynomials 2x3 + ax2 + 3x - 5 and x3 + x2 - 2x + a leave the same remainder when divided by (x - 2), find the value of a. Also, find the remainder in each case.

On dividing (ax³ + 9x² + 4x - 10) by (x + 3), we get 5 as remainder. Find the value of a.

Using remainder theorem, find the remainder when:
f(x) = 9x² - 6x + 2 is divided by (3x - 2).

Using remainder theorem, find the remainder when:
f(x) = 8x² - 2x - 15 is divided by (2x + 3).

Using Remainder Theorem, find the value of k if on dividing 2x³ + 3x² - kx + 5 by (x - 2), leaves a remainder 7.

If the polynomials 2x³ + ax² + 3x - 5 and x³ + x² - 2x + a leave the same remainder when divided by (x - 2), find the value of a. Also, find the remainder in each case.