To find the remainder when the polynomial 5x² + 10x + 15 is divided by x – 5, we can use the Remainder Theorem.
The Remainder Theorem states that the remainder of the division of a polynomial f(x) by x – c is equal to f(c). In this case, our polynomial f(x) is 5x² + 10x + 15, and we are dividing by x – 5, which means c = 5.
Now, let’s calculate f(5):
- First, substitute 5 for x in the polynomial:
- f(5) = 5(5)² + 10(5) + 15
- f(5) = 5(25) + 50 + 15
- f(5) = 125 + 50 + 15
- f(5) = 190
Therefore, the remainder when 5x² + 10x + 15 is divided by x – 5 is 190.
Summary:
The remainder of the polynomial 5x² + 10x + 15 when divided by x – 5 is 190.