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

For x = 2, the value of 2x 3 - 7x 2 - 3x + 18, = 2(2) 3 - 7(2) 2 - 3(2) + 18 = 16 - 28 - 6 + 18 = 34 - 34 = 0. Hence, (x - 2) is the factor of 2x 3 - 7x 2 - 3x + 18. On dividing, 2x 3 - 7x 2 - 3x + 18 by (x - 2), we get quotient = 2x 2 - 3x - 9. Factorising 2x 2 - 3x - 9, = 2x 2 - 6x + 3x - 9 = 2x(x - 3) + 3(x - 3) = (2x + 3)(x - 3). ∴ 2x 2 - 3x - 9 = (2x + 3)(x - 3). ∴ f(x) = 2x 3 - 7x 2 - 3x + 18 = (x - 2)(2x + 3)(x - 3). f(x) = 0, if (x - 2) = 0, (2x + 3) = 0 or x - 3 = 0. x - 2 = 0 ⇒ x =2, 2x + 3 = 0 ⇒ x = -, x - 3 = 0 ⇒ x = 3. Hence, 2x 3 - 7x 2 - 3x + 18 = (x - 2)(2x + 3)(x - 3), values for which f(x) = 0 are 2, 3, .

Using the remainder theorem, factorise each of the following completely :
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Using the Remainder Theorem, factorise the expression 3x³ + 10x² + x - 6. Hence, solve the equation 3x³ + 10x² + x - 6 = 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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The expression 4x³ - bx² + x - c leaves remainders 0 and 30 when divided by x + 1 and 2x - 3 respectively. Calculate the values of b and c. Hence, factorise the expression completely.

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Mathematics

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

Factorisation

Related Questions

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

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

The expression 4x³ - bx² + x - c leaves remainders 0 and 30 when divided by x + 1 and 2x - 3 respectively. Calculate the values of b and c. Hence, factorise the expression completely.

Mathematics

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

Factorisation

Related Questions

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

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

The expression 4x3 - bx2 + x - c leaves remainders 0 and 30 when divided by x + 1 and 2x - 3 respectively. Calculate the values of b and c. Hence, factorise the expression completely.

Factorise the expression
f(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 the expression 3x³ + 10x² + x - 6. Hence, solve the equation 3x³ + 10x² + x - 6 = 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).

The expression 4x³ - bx² + x - c leaves remainders 0 and 30 when divided by x + 1 and 2x - 3 respectively. Calculate the values of b and c. Hence, factorise the expression completely.