To find the remainder when the polynomial 6x² + 11x + 7 is divided by 2x + 1, we can use the Remainder Theorem, which states that the remainder of the division of a polynomial f(x) by a linear divisor ax + b is equal to f(-b/a).
In our case, we have:
- Polynomial: f(x) = 6x² + 11x + 7
- Divisor: 2x + 1
- Here, a = 2 and b = 1, so we will substitute x = -1/2 into the polynomial.
Let’s calculate f(-1/2):
f(-1/2) = 6(-1/2)² + 11(-1/2) + 7
Calculating each term:
- First term: 6(-1/2)² = 6(1/4) = 6/4 = 3/2
- Second term: 11(-1/2) = -11/2
- Now, adding the constant term: f(-1/2) = 3/2 – 11/2 + 7
Combining the fractions:
- 3/2 – 11/2 = -8/2 = -4
- So, -4 + 7 = 3
Thus, the remainder when 6x² + 11x + 7 is divided by 2x + 1 is 3.
In conclusion, the answer is 3.