What is the remainder when (2x³ + 4x² - 32x + 18) ÷ (x + 3) ?

Solution:

An expression having non-zero coefficients comprised of variables, constants and exponents is called polynomials.

To find the remainder, we will do long division.

(2 x³ + 4 x² - 32 x + 18) ÷ (x + 3)

By division algorithm,

Dividend = Divisor × Quotient + Remainder

⇒ ( 2 x³ + 4 x² - 32 x + 18 ) = ( x + 3 ) × ( 2 x² - 2 x - 26 ) + 96

⇒ ( 2 x³ + 4 x² - 32 x + 18 ) = ( 2 x³ - 2 x² - 26 x + 6 x² - 6 x - 78 ) + 96

⇒ ( 2 x³ + 4 x² - 32 x + 18 ) = ( 2 x³ + 4 x²  - 32 x - 78 ) + 96

⇒ ( 2 x³ + 4 x² - 32 x + 18 ) = ( 2 x³ + 4 x² - 32 x + 18 ) 

⇒ LHS = RHS 

You can use Cuemath's Polynomial Calculator to divide the polynomials.

Thus, the remainder when the polynomial (2x³ + 4x² - 32 x + 18) is divided by (x + 3) is 96.

What is the remainder when (2x³ + 4x² - 32x + 18) ÷ (x + 3) ?

Summary:

The remainder when the polynomial (2x³ + 4x² - 32x + 18) divided by (x + 3) is 96.