For what value of a is the polynomial (2x³ + ax² + 11x + a + 3) exactly divisible by (2x - 1)?
Factorisation
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Question

For what value of a is the polynomial (2x^3 + ax^2 + 11x + a + 3) exactly divisible by (2x − 1)?

KnowledgeBoat · Accepted Answer

Let f(x) = 2x3 + ax2 + 11x + a + 3. Given, Factor : 2x - 1 ⇒ 2x - 1 = 0 ⇒ 2x = 1 ⇒ x = Thus, on dividing 2x3 + ax2 + 11x + a + 3 by 2x - 1, remainder = 0. Hence, the value of a = -7.

Mathematics

For what value of a is the polynomial (2x³ + ax² + 11x + a + 3) exactly divisible by (2x - 1)?

Factorisation

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Mathematics

For what value of a is the polynomial (2x3 + ax2 + 11x + a + 3) exactly divisible by (2x - 1)?

Factorisation

Related Questions

Use factor theorem to show that (x + 2) and (2x - 3) are factors of (2x2 + x - 6).

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What must be subtracted from 16x3 - 8x2 + 4x + 7 so that the resulting expression has (2x + 1) as a factor?

For what value of a is the polynomial (2x³ + ax² + 11x + a + 3) exactly divisible by (2x - 1)?

Use factor theorem to show that (x + 2) and (2x - 3) are factors of (2x² + x - 6).

Find the value of a so that (x + 6) is a factor of the polynomial (x³ + 5x² - 4x + a).

What must be subtracted from the polynomial x³ + x² - 2x + 1, so that the result is exactly divisible by (x - 3)?

What must be subtracted from 16x³ - 8x² + 4x + 7 so that the resulting expression has (2x + 1) as a factor?