Question

What is the remainder when the polynomial 4x^2 + 10x - 4 is divided by 2x - 1 if the options are 3, 2, -1, and 0?

a) 3
b) 2
c) -1
d) 0

Answer 1

Using the Remainder Theorem, the remainder when the polynomial 4x^2 + 10x - 4 is divided by 2x - 1 is calculated to be 2 by substituting x = 1/2 into the polynomial.

Step-by-step explanation:

To find the remainder when the polynomial 4x^2 + 10x - 4 is divided by 2x - 1, we can use the Remainder Theorem. This theorem states that the remainder of a polynomial f(x) divided by x - k is f(k). In this case, k is the solution to 2x - 1 = 0, which is x = 1/2. Substituting x with 1/2 into the polynomial, we get:

• 4(1/2)^2 + 10(1/2) - 4
• 4(1/4) + 5 - 4
• 1 + 5 - 4
• 6 - 4
• 2

Therefore, the remainder when 4x^2 + 10x - 4 is divided by 2x - 1 is 2.