What is the remainder when (2x³ + 4x² - 32x - 40) ÷ (x - 4)?

Solution:

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

To find the remainder, we will do long division of polynomial.

(2 x³ + 4 x² - 32 x - 40) ÷ (x - 4)

By division algorithm,

Dividend = Divisor × Quotient + Remainder

⇒ (2 x³ + 4 x² - 32 x - 40) = (x - 4) × (2 x² + 12 x + 16) + 24

⇒ (2 x³ + 4 x² - 32 x - 40) = (2 x³ + 12 x² + 16 x - 8 x² - 48 x - 64) + 24

⇒ (2 x³ + 4 x² - 32 x - 40) = (2 x³ + 4 x²  - 32 x - 64 ) + 24

⇒ (2 x³ + 4 x² - 32 x - 40) = (2 x³ + 4 x² - 32 x - 40) 

⇒ LHS = RHS 

Thus, the remainder when the polynomial 2 x³ + 4 x² - 32 x - 40 divided by x - 4 is 24.

What is the remainder when (2x³ + 4x² - 32x - 40) ÷ (x - 4)?

Summary:

The remainder when the polynomial 2x³ + 4x² - 32x - 40 divided by x - 4 is 24.