# What is the remainder when (2x^{3} + 4x^{2} - 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 x^{3} + 4 x^{2} - 32 x - 40) ÷ (x - 4)

Dividend = Divisor × Quotient + Remainder

⇒ (2 x^{3} + 4 x^{2} - 32 x - 40) = (x - 4) × (2 x^{2} + 12 x + 16) + 24

⇒ (2 x^{3} + 4 x^{2} - 32 x - 40) = (2 x^{3} + 12 x^{2} + 16 x - 8 x^{2 }- 48 x - 64) + 24

⇒ (2 x^{3} + 4 x^{2} - 32 x - 40) = (2 x^{3} + 4 x^{2} ^{ }- 32 x - 64 ) + 24

⇒ (2 x^{3} + 4 x^{2} - 32 x - 40) = (2 x^{3} + 4 x^{2} - 32 x - 40)

⇒ LHS = RHS

Thus, the remainder when the polynomial 2 x^{3} + 4 x^{2} - 32 x - 40 divided by x - 4 is 24.

## What is the remainder when (2x^{3} + 4x^{2} - 32x - 40) ÷ (x - 4)?

**Summary:**

The remainder when the polynomial 2x^{3} + 4x^{2} - 32x - 40 divided by x - 4 is 24.

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