Questions: What polynomial must be added to -3c^2 + 3 - 6c in order to get a sum of 2c^2 - c + 5?

What polynomial must be added to -3c^2 + 3 - 6c in order to get a sum of 2c^2 - c + 5?
Transcript text: 6. What polynomial must be added to $-3 c^{2}+3-6 c$ in order to get a sum of $2 c^{2}-c+5$ ?
failed

Solution

failed
failed

Solution Steps

To find the polynomial that must be added to 3c2+36c-3c^2 + 3 - 6c to get 2c2c+52c^2 - c + 5, we need to subtract the first polynomial from the second polynomial. This will give us the polynomial that, when added to the first, results in the second.

Step 1: Identify the Given Polynomials

We are given two polynomials:

  1. The polynomial to which we need to add another polynomial: 3c26c+3-3c^2 - 6c + 3.
  2. The desired sum of the two polynomials: 2c2c+52c^2 - c + 5.
Step 2: Set Up the Equation

To find the polynomial that must be added, we set up the equation: First Polynomial+Polynomial to Add=Desired Sum \text{First Polynomial} + \text{Polynomial to Add} = \text{Desired Sum} Substituting the given polynomials, we have: (3c26c+3)+Polynomial to Add=2c2c+5 (-3c^2 - 6c + 3) + \text{Polynomial to Add} = 2c^2 - c + 5

Step 3: Solve for the Polynomial to Add

To find the polynomial to add, we subtract the first polynomial from the desired sum: Polynomial to Add=(2c2c+5)(3c26c+3) \text{Polynomial to Add} = (2c^2 - c + 5) - (-3c^2 - 6c + 3)

Step 4: Simplify the Expression

Simplifying the expression, we get: Polynomial to Add=2c2c+5+3c2+6c3 \text{Polynomial to Add} = 2c^2 - c + 5 + 3c^2 + 6c - 3 Combine like terms: Polynomial to Add=(2c2+3c2)+(c+6c)+(53) \text{Polynomial to Add} = (2c^2 + 3c^2) + (-c + 6c) + (5 - 3) Polynomial to Add=5c2+5c+2 \text{Polynomial to Add} = 5c^2 + 5c + 2

Final Answer

The polynomial that must be added is 5c2+5c+2\boxed{5c^2 + 5c + 2}.

Was this solution helpful?
failed
Unhelpful
failed
Helpful