What is the result of adding the polynomials (3x^2 + 2x + 1) and (4x^2 - x + 5)?
Practice Questions
Q1
What is the result of adding the polynomials (3x^2 + 2x + 1) and (4x^2 - x + 5)?
7x^2 + x + 6
7x^2 + 3x + 6
x^2 + x + 6
7x^2 + 2x + 5
Questions & Step-by-Step Solutions
What is the result of adding the polynomials (3x^2 + 2x + 1) and (4x^2 - x + 5)?
Step 1: Write down the two polynomials you want to add: (3x^2 + 2x + 1) and (4x^2 - x + 5).
Step 2: Identify the like terms in both polynomials. Like terms are terms that have the same variable raised to the same power.
Step 3: Group the like terms together: (3x^2 + 4x^2), (2x - x), and (1 + 5).
Step 4: Add the coefficients of the like terms: For x^2 terms, add 3 and 4 to get 7. For x terms, add 2 and -1 to get 1. For constant terms, add 1 and 5 to get 6.
Step 5: Write the result by combining the sums of the like terms: 7x^2 + 1x + 6.
Step 6: Simplify the expression if possible. Since 1x can be written as x, the final result is 7x^2 + x + 6.
