Question

Based on the polynomial remainder theorem, what is the value of the function when x=-5

f(x)=x^4+9x^3+17x^2-8x+50

Answer 1

Answer: 15

Explanation:

Using synthetic division:

-5 | 1 9 17 -8 50

| ↓ -5 -20 15 -35

1 4 -3 7 15 ← this is the remainder

Check:

f(x) = x⁴ + 9x³ + 17x² - 8x + 50

f(-5) = (-5)⁴ + 9(-5)³ + 17(-5)² - 8(-5) + 50

= 625 - 1125 + 425 + 40 + 50

= 15