Using the remainder theorem, factorise each of the following completely :
x³ + x² - 4x - 4

Question

Using the remainder theorem, factorise each of the following completely : x³ + x² - 4x - 4

KnowledgeBoat · Accepted Answer

For x = -1 the value of x³ + x² - 4x - 4 = (-1)³ + (-1)² - 4(-1) - 4 = -1 + 1 + 4 - 4 = 0. Hence, (x + 1) is the factor of x³ + x² - 4x - 4. On dividing x³ + x² - 4x - 4 by (x + 1), we get, quotient = x² - 4 Factorising x² - 4, = (x)² - 4 = (x + 2)(x - 2) ∴ x² - 4 = (x - 2)(x + 2) Hence, x³ + x² - 4x - 4 = (x + 1)(x + 2)(x - 2).

Mathematics

Using the remainder theorem, factorise each of the following completely :
x³ + x² - 4x - 4

Factorisation

Related Questions

Using the remainder theorem, factorise each of the following completely :
3x³ + 2x² - 23x - 30

Using the remainder theorem, factorise each of the following completely :
4x³ + 7x² - 36x - 63

Using the Remainder Theorem, factorise the expression 3x³ + 10x² + x - 6. Hence, solve the equation 3x³ + 10x² + x - 6 = 0.

Factorise the expression
f(x) = 2x³ - 7x² - 3x + 18.
Hence, find all possible values of x for which f(x) = 0.

Mathematics

Using the remainder theorem, factorise each of the following completely :x3 + x2 - 4x - 4

Factorisation

Related Questions

Using the remainder theorem, factorise each of the following completely :3x3 + 2x2 - 23x - 30

Using the remainder theorem, factorise each of the following completely :4x3 + 7x2 - 36x - 63

Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x - 6. Hence, solve the equation 3x3 + 10x2 + x - 6 = 0.

Factorise the expressionf(x) = 2x3 - 7x2 - 3x + 18.Hence, find all possible values of x for which f(x) = 0.

Using the remainder theorem, factorise each of the following completely :
x³ + x² - 4x - 4

Using the remainder theorem, factorise each of the following completely :
3x³ + 2x² - 23x - 30

Using the remainder theorem, factorise each of the following completely :
4x³ + 7x² - 36x - 63

Using the Remainder Theorem, factorise the expression 3x³ + 10x² + x - 6. Hence, solve the equation 3x³ + 10x² + x - 6 = 0.

Factorise the expression
f(x) = 2x³ - 7x² - 3x + 18.
Hence, find all possible values of x for which f(x) = 0.