To find the remainder when the polynomial 5x² + 10x + 15 is divided by x + 5, we can use the Remainder Theorem. According to this theorem, the remainder of the division of a polynomial f(x) by a linear divisor x – c is simply f(c).
In this case, the divisor is x + 5, which can be rewritten as x – (-5). Therefore, we need to evaluate the polynomial at x = -5.
Let’s compute f(-5) where f(x) = 5x² + 10x + 15:
- f(-5) = 5(-5)² + 10(-5) + 15
- f(-5) = 5(25) – 50 + 15
- f(-5) = 125 – 50 + 15
- f(-5) = 125 – 35
- f(-5) = 90
Thus, the remainder when 5x² + 10x + 15 is divided by x + 5 is 90.