What is the remainder when the polynomial 5x² + 10x − 15 is divided by x + 5?

Solution:

A quadratic expression is in the form of ax² + bx + c. 

Let's find the remainder when 5x² + 10x − 15 is divided by x + 5.

We will divide the polynomial by the long division method.

(5x² + 10x − 15) ÷  (x + 5)

We can verify this by division algorithm: Dividend = Divisor × Quotient + Remainder

So, we will show that 5x² + 10x − 15 = (x + 5) (5x - 15) + 60

⇒ (x + 5) (5x - 15) + 60 = 5x²  - 15x + 25x − 75 + 60 = 5x² + 10x − 15

LHS = RHS

Hence Proved