Finding the Remainder
To find the remainder of the polynomial 4x³ + 2x² + 18x + 38 when divided by x – 3, we can utilize the Remainder Theorem. According to this theorem, the remainder of the division of a polynomial f(x) by x – c is simply f(c).
Step 1: Determine f(c)
In this case, our polynomial f(x) is 4x³ + 2x² + 18x + 38, and we want to find the remainder when divided by x – 3. Thus, we need to evaluate f(3).
Step 2: Calculate f(3)
Let’s substitute x = 3 into the polynomial:
- f(3) = 4(3)³ + 2(3)² + 18(3) + 38
- = 4(27) + 2(9) + 54 + 38
- = 108 + 18 + 54 + 38
- = 218
Step 3: Result
So, the remainder when dividing the polynomial 4x³ + 2x² + 18x + 38 by x – 3 is 218.
Conclusion
In summary, using the Remainder Theorem, we find that the remainder of the polynomial 4x³ + 2x² + 18x + 38 when divided by x – 3 is 218.