What is the result when 2x³ - 9x² + 11x - 6 is divided by x - 3?

Solution:

A polynomial is a type of expression in which the exponents of all variables should be a whole number.

Given: Dividend = 2x³ - 9x² + 11x - 6, Divisor = x - 3

We will use the long division of polynomials to divide the two polynomials

Let's look into the division shown below:

Thus, we see that the quotient is 2x² - 3x + 2

The Division algorithm for polynomials says if p(x) and g(x) are the two polynomials, where g(x) ≠ 0, we can write the division of polynomials as:

p(x) = q(x) × g(x) + r(x) ---------------- (1)

Where,

•  p(x) is the dividend.
•  q(x) is the quotient.
•  g(x) is the divisor.
•  r(x) is the remainder.

Verification:

p(x) = 2x³ - 9x² + 11x - 6, g(x) = x - 3, q(x) = 2x² - 3x + 2, r(x) = 0

Substituting the values in RHS of (1) we get,

RHS = q(x) × g(x) + r(x)

RHS = (x - 3) (2x² - 3x + 2)

RHS = 2x³ - 9x² + 11x - 6 = p(x)

Thus, we see that LHS = RHS

We can also use Cuemath's online polynomial calculator to perform different arithmetic operations on polynomials.

Hence, when 2x³ - 9x² + 11x - 6 is divided by x - 3 we get 2x² - 3x + 2.

What is the result when 2x³ - 9x² + 11x - 6 is divided by x - 3?

Summary:

The result when 2x³ - 9x² + 11x - 6 is divided by x - 3 is equal to 2x² - 3x + 2.