Using Factor Theorem, show that : (3x + 2) is a factor of 3x 3 + 2x 2 - 3x - 2. Hence, factorise the expression 3x 3 + 2x 2 - 3x - 2 completely.

3x + 2 = 0 ⇒ x = . Remainder = The value of 3x 3 + 2x 2 - 3x - 2 at x = . Hence, 3x + 2 is a factor of 3x 3 + 2x 2 - 3x - 2. Now dividing, 3x 3 + 2x 2 - 3x - 2 by 3x + 2, we get quotient = x 2 - 1. Factorising, x 2 - 1 = (x) 2 - (1) 2 = (x + 1)(x - 1). ∴ 3x 3 + 2x 2 - 3x - 2 = (3x + 2)(x + 1)(x - 1). Hence, 3x 3 + 2x 2 - 3x - 2 = (3x + 2)(x + 1)(x - 1).

The polynomial px³ + 4x² - 3x + q is completely divisible by x² - 1; find the values of p and q. Also for these values of p and q factorize the given polynomial completely.

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When the polynomial x³ + 2x² - 5ax - 7 is divided by (x - 1), the remainder is A and when the polynomial x³ + ax² - 12x + 16 is divided by (x + 2), the remainder is B. Find the value of 'a' if 2A + B = 0.

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(3x + 5) is a factor of the polynomial (a - 1)x³ + (a + 1)x² - (2a + 1)x - 15. Find the value of 'a'. For this value of 'a', factorise the given polynomial completely.

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Using remainder theorem, find the value of k if on dividing 2x³ + 3x² - kx + 5 by (x - 2) leaves a remainder 7.

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Mathematics

Using Factor Theorem, show that :
(3x + 2) is a factor of 3x³ + 2x² - 3x - 2. Hence, factorise the expression 3x³ + 2x² - 3x - 2 completely.

Factorisation

Related Questions

The polynomial px³ + 4x² - 3x + q is completely divisible by x² - 1; find the values of p and q. Also for these values of p and q factorize the given polynomial completely.

When the polynomial x³ + 2x² - 5ax - 7 is divided by (x - 1), the remainder is A and when the polynomial x³ + ax² - 12x + 16 is divided by (x + 2), the remainder is B. Find the value of 'a' if 2A + B = 0.

(3x + 5) is a factor of the polynomial (a - 1)x³ + (a + 1)x² - (2a + 1)x - 15. Find the value of 'a'. For this value of 'a', factorise the given polynomial completely.

Using remainder theorem, find the value of k if on dividing 2x³ + 3x² - kx + 5 by (x - 2) leaves a remainder 7.

Mathematics

Using Factor Theorem, show that :(3x + 2) is a factor of 3x3 + 2x2 - 3x - 2. Hence, factorise the expression 3x3 + 2x2 - 3x - 2 completely.

Factorisation

Related Questions

The polynomial px3 + 4x2 - 3x + q is completely divisible by x2 - 1; find the values of p and q. Also for these values of p and q factorize the given polynomial completely.

When the polynomial x3 + 2x2 - 5ax - 7 is divided by (x - 1), the remainder is A and when the polynomial x3 + ax2 - 12x + 16 is divided by (x + 2), the remainder is B. Find the value of 'a' if 2A + B = 0.

(3x + 5) is a factor of the polynomial (a - 1)x3 + (a + 1)x2 - (2a + 1)x - 15. Find the value of 'a'. For this value of 'a', factorise the given polynomial completely.

Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 - kx + 5 by (x - 2) leaves a remainder 7.

Using Factor Theorem, show that :
(3x + 2) is a factor of 3x³ + 2x² - 3x - 2. Hence, factorise the expression 3x³ + 2x² - 3x - 2 completely.

The polynomial px³ + 4x² - 3x + q is completely divisible by x² - 1; find the values of p and q. Also for these values of p and q factorize the given polynomial completely.

When the polynomial x³ + 2x² - 5ax - 7 is divided by (x - 1), the remainder is A and when the polynomial x³ + ax² - 12x + 16 is divided by (x + 2), the remainder is B. Find the value of 'a' if 2A + B = 0.

(3x + 5) is a factor of the polynomial (a - 1)x³ + (a + 1)x² - (2a + 1)x - 15. Find the value of 'a'. For this value of 'a', factorise the given polynomial completely.

Using remainder theorem, find the value of k if on dividing 2x³ + 3x² - kx + 5 by (x - 2) leaves a remainder 7.