Prove that (5x + 4) is a factor of 5x³ + 4x² - 5x - 4. Hence, factorise the given polynomial completely.
Factorisation
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Question

Prove that (5x + 4) is a factor of 5x³ + 4x² - 5x - 4. Hence, factorise the given polynomial completely.

KnowledgeBoat · Accepted Answer

By factor theorem (x - b) is a factor of f(x), if f(b) = 0. f(x) = 5x³ + 4x² - 5x - 4 Given, (5x + 4) or 5(x - (-)) is a factor of f(x) hence, let's find f(-). Since, f(-) = 0, hence (5x + 4) is a factor of f(x). Now, factorising the equation 5x³ + 4x² - 5x - 4 Hence, 5x³ + 4x² - 5x - 4 = (x - 1)(x + 1)(5x + 4).

Mathematics

Prove that (5x + 4) is a factor of 5x³ + 4x² - 5x - 4. Hence, factorise the given polynomial completely.

Factorisation

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Mathematics

Prove that (5x + 4) is a factor of 5x3 + 4x2 - 5x - 4. Hence, factorise the given polynomial completely.

Factorisation

Related Questions

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If (2x - 3) is a factor of 6x² + x + a, find the value of a. With this value of a, factorise the given expression.

When 3x² - 5x + p is divided by (x - 2), the remainder is 3. Find the value of p. Also factorise the polynomial 3x² - 5x + p - 3.

Use factor theorem to factorise the following polynomials completely :
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(iii) 2x³ - x² - 13x - 6

If x³ - 2x² + px + q has a factor (x + 2) and leaves a remainder 9 when divided by (x + 1), find the values of p and q. With these values of p and q, factorise the given polynomial completely.