Questions: 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 $2 c^{2}-c+5$ ?
Solution
Solution Steps
To find the polynomial that must be added to −3c2+3−6c to get 2c2−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:
The polynomial to which we need to add another polynomial: −3c2−6c+3.
The desired sum of the two polynomials: 2c2−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
Substituting the given polynomials, we have:
(−3c2−6c+3)+Polynomial to Add=2c2−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=(2c2−c+5)−(−3c2−6c+3)
Step 4: Simplify the Expression
Simplifying the expression, we get:
Polynomial to Add=2c2−c+5+3c2+6c−3
Combine like terms:
Polynomial to Add=(2c2+3c2)+(−c+6c)+(5−3)Polynomial to Add=5c2+5c+2