Use the remainder theorem to factorise the expression 2x 3 + 9x 2 + 7x - 6. Hence, solve the equation 2x 3 + 9x 2 + 7x - 6.

For x = -2, the value of the given expression = 2(-2) 3 + 9(-2) 2 + 7(-2) - 6 = 2 × -8 + 9 × 4 - 14 - 6 = -16 + 36 - 14 - 6 = -36 + 36 = 0. ⇒ x + 2 is a factor of 2x 3 + 9x 2 + 7x - 6. Now dividing 2x 3 + 9x 2 + 7x - 6 by (x + 2), we get quotient = 2x 2 + 5x - 3 ∴ 2x 3 + 9x 2 + 7x - 6 = (x + 2)(2x 2 + 5x - 3) = (x + 2)(2x 2 + 6x - x - 3) = (x + 2)[2x(x + 3) - 1(x + 3)] = (x + 2)(2x - 1)(x + 3). ∴ (x + 2), (2x - 1) and (x + 3) are the factors of 2x 3 + 9x 2 + 7x - 6. ⇒ x + 2 = 0 ⇒ x = -2 ⇒ 2x - 1 = 0 ⇒ x = ⇒ x + 3 = 0 ⇒ x = -3. Hence, 2x 3 + 9x 2 + 7x - 6 = (x + 2)(2x - 1)(x + 3) and x = -2, -3, .

View Answer Bookmark Now

Given that x + 2 and x - 3 are factors of x³ + ax + b. Calculate the values of a and b. Also, find the remaining factor.

View Answer Bookmark Now

When 2x³ + 5x² - 2x + 8 is divided by (x - a) the remainder is 2a³ + 5a². Find the value of a.

View Answer Bookmark Now

What number should be added to x³ - 9x² - 2x + 3 so that the remainder may be 5 when divided by (x - 2) ?

View Answer Bookmark Now

Mathematics

Use the remainder theorem to factorise the expression 2x³ + 9x² + 7x - 6. Hence, solve the equation 2x³ + 9x² + 7x - 6.

Factorisation

Related Questions

Given that x + 2 and x - 3 are factors of x³ + ax + b. Calculate the values of a and b. Also, find the remaining factor.

When 2x³ + 5x² - 2x + 8 is divided by (x - a) the remainder is 2a³ + 5a². Find the value of a.

What number should be added to x³ - 9x² - 2x + 3 so that the remainder may be 5 when divided by (x - 2) ?

Mathematics

Use the remainder theorem to factorise the expression 2x3 + 9x2 + 7x - 6. Hence, solve the equation 2x3 + 9x2 + 7x - 6.

Factorisation

Related Questions

Given that x + 2 and x - 3 are factors of x3 + ax + b. Calculate the values of a and b. Also, find the remaining factor.

When 2x3 + 5x2 - 2x + 8 is divided by (x - a) the remainder is 2a3 + 5a2. Find the value of a.

What number should be added to x3 - 9x2 - 2x + 3 so that the remainder may be 5 when divided by (x - 2) ?

Use the remainder theorem to factorise the expression 2x³ + 9x² + 7x - 6. Hence, solve the equation 2x³ + 9x² + 7x - 6.

Given that x + 2 and x - 3 are factors of x³ + ax + b. Calculate the values of a and b. Also, find the remaining factor.

When 2x³ + 5x² - 2x + 8 is divided by (x - a) the remainder is 2a³ + 5a². Find the value of a.

What number should be added to x³ - 9x² - 2x + 3 so that the remainder may be 5 when divided by (x - 2) ?