What is the remainder when (x³ - 4 x² - 12 x + 9) is divided by (x + 2) ?

Solution:

An expression having non-zero coefficients comprising variables, constants and exponents is called a polynomial.

To find the remainder, we will use the long division method.

(x³ - 4 x² - 12 x + 9) ÷ (x + 2)

By division algorithm, let's verify,

Dividend = Divisor × Quotient + Remainder

⇒ ( x³ - 4 x² - 12 x + 9 ) = ( x + 2) × ( x² - 6 x ) + 9

⇒ ( x³ - 4 x² - 12 x + 9 ) = ( x³ - 6 x² + 2 x² - 12 x ) + 9

⇒ ( x³ - 4 x² - 12 x + 9 ) = ( x³ - 4 x² - 12 x ) + 9

⇒ ( x³ - 4 x² - 12 x + 9 ) = ( x³ - 4 x² - 12 x + 9 ) 

⇒ LHS = RHS 

You can use a polynomial calculator to divide the polynomials.

Thus, the remainder when the polynomial (x³ - 4 x² - 12 x + 9) is divided by x + 2 is 9 .

What is the remainder when (x³ - 4 x² - 12 x + 9) is divided by (x + 2) ?

Summary:

The remainder when the polynomial (x³ - 4 x² - 12 x + 9) is divided by x + 2 is 9 .