Final answer:
By expanding and simplifying the given equation, we find that the values of the constants are c = 2/3 and d = -4/3 by matching coefficients.
Step-by-step explanation:
The student has provided an equation that requires finding the values of the constants c and d. To do this, we need to expand and simplify the given equation c(x + 3) = 2(x - 1) + dx + 4. We'll expand both sides and collect like terms, matching the coefficients of the corresponding terms on each side of the equation.
First, expand the left side to get cx + 3c. Next, expand the right side to get 2x - 2 + dx + 4. Then combine like terms on the right side to give (2 + d)x + 2. Now, we have cx + 3c = (2 + d)x + 2. Matching coefficients, we get two equations: c = 2 + d and 3c = 2. Solving for c in the second equation, we get c = 2/3. Plugging this value into the first equation, we solve for d, yielding d = c - 2 = 2/3 - 2 = -4/3.
To find the values of constants c and d, we can start by expanding the given equation: c(x^3) + 2(x-1) = dx^4.
Next, distribute the c and 2 to each term: cx^3 + 2x - 2 = dx^4.
Now, rearrange the terms and set the equation equal to 0: dx^4 - cx^3 - 2x + 2 = 0.
By comparing the coefficients of like terms, we can set up a system of equations to solve for c and d. In this case, c = -2 and d = 1.