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Algebra: Polynomial Operations - Sum, Product, and Division
Published on July 29, 2026
Algebra
Learn how to perform polynomial addition, multiplication, and division with given polynomials P(x) and Q(x).
Question
given that P(x)=x-1, q(x)=x^3+3x-4, evalulate the following: a) P(x)+q(x). B) p(x) times Q(x). C) q(x) divided by P(x)
Answer
Given the polynomials:
We will evaluate each part step by step.
a)
To find the sum, we add the two expressions together and combine like terms:
Group the terms by their powers of
Answer for a):
b)
To find the product, we multiply each term in
Distribute
Distribute
Now, combine the results:
Answer for b):
c)
We need to divide
Using Synthetic Division:
The root of
The coefficients of
The root of
The coefficients of
Set up the synthetic division:
Step-by-step breakdown:
- Bring down the
. - Multiply
. Add to : . - Multiply
. Add to : . - Multiply
. Add to : .
The resulting coefficients are
Answer for c):