Show that (x - 1) is a factor of x 3 - 7x 2 + 14x - 8. Hence, completely factorise the given expression.

x - 1 = 0 ⇒ x = 1. Substituting x = 1 in x 3 - 7x 2 + 14x - 8 we get, = (1) 3 - 7(1) 2 + 14(1) - 8 = 1 - 7 + 14 - 8 = 15 - 15 = 0. Since, remainder = 0. Hence, (x - 1) is a factor of x 3 - 7x 2 + 14x - 8. On dividing, x 3 - 7x 2 + 14x - 8 by (x - 1), we get, quotient = x 2 - 6x + 8. Factorising x 2 - 6x + 8, = x 2 - 4x - 2x + 8 = x(x - 4) - 2(x - 4) = (x - 2)(x - 4). Hence, x 3 - 7x 2 + 14x - 8 = (x - 1)(x - 2)(x - 4).

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

Show that (x - 1) is a factor of x³ - 7x² + 14x - 8. Hence, completely factorise the given expression.

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

Show that (x - 1) is a factor of x3 - 7x2 + 14x - 8. Hence, completely factorise the given expression.

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.

Show that (x - 1) is a factor of x³ - 7x² + 14x - 8. Hence, completely factorise the given expression.

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.