Using the Remainder Theorem, factorise the expression 3x 3 + 10x 2 + x - 6. Hence, solve the equation 3x 3 + 10x 2 + x - 6 = 0.

For x = -1, the value of 3x 3 + 10x 2 + x - 6, = 3(-1) 3 + 10(-1) 2 + (-1) - 6 = 3(-1) + 10(1) - 7 = 10 - 10 = 0. Hence, (x + 1) is the factor of 3x 3 + 10x 2 + x - 6. On dividing 3x 3 + 10x 2 + x - 6 by (x + 1), we get, quotient = 3x 2 + 7x - 6 Factorising 3x 2 + 7x - 6, = 3x 2 + 9x - 2x - 6 = 3x(x + 3) - 2(x + 3) = (3x - 2)(x + 3). ∴ 3x 2 + 7x - 6 = (3x - 2)(x + 3). Hence, 3x 3 + 10x 2 + x - 6 = (x + 1)(3x - 2)(x + 3).

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

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

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

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Given that x - 2 and x + 1 are factors of f(x) = x³ + 3x² + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).

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Mathematics

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

Factorisation

Related Questions

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

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

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

Given that x - 2 and x + 1 are factors of f(x) = x³ + 3x² + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).

Mathematics

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

Factorisation

Related Questions

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

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

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

Given that x - 2 and x + 1 are factors of f(x) = x3 + 3x2 + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).

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

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

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

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

Given that x - 2 and x + 1 are factors of f(x) = x³ + 3x² + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).