What is the result of adding the polynomials P(x) = 3x^2 + 2x + 1 and Q(x) = x^2
Practice Questions
Q1
What is the result of adding the polynomials P(x) = 3x^2 + 2x + 1 and Q(x) = x^2 - x + 4?
4x^2 + x + 5
4x^2 + 3x + 5
2x^2 + x + 5
3x^2 + x + 5
Questions & Step-by-Step Solutions
What is the result of adding the polynomials P(x) = 3x^2 + 2x + 1 and Q(x) = x^2 - x + 4?
Step 1: Write down the two polynomials you want to add: P(x) = 3x^2 + 2x + 1 and Q(x) = x^2 - x + 4.
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. The like terms are: 3x^2 from P(x) and x^2 from Q(x), 2x from P(x) and -x from Q(x), and 1 from P(x) and 4 from Q(x).
Step 4: Add the coefficients of the like terms together. For the x^2 terms: 3 + 1 = 4, for the x terms: 2 - 1 = 1, and for the constant terms: 1 + 4 = 5.
Step 5: Write the result as a new polynomial by combining the sums of the like terms: 4x^2 + 1x + 5.
Step 6: Simplify the polynomial if necessary. In this case, 1x can be written simply as x, so the final result is 4x^2 + x + 5.
