Question

1. Compare the strengths and weaknesses of the horizontal and vertical methods for adding and subtracting polynomials. Include common errors to watch out for when using each of these methods.

2. Explain why you cannot use algebra tiles to model the multiplication of a linear polynomial by a quadratic polynomial.

As an added challenge, develop a model similar to algebra tiles that will allow you to show this multiplication. Describe an example of your model for the product (x + 1)(x2 + 2x + 2).

3. Imagine that you are teaching a new student how to multiply polynomials. Explain how multiplying polynomials is similar to multiplying integers. Then describe the key differences between the two.

4. If you multiply a binomial by a binomial, how many terms are in the product (before combining like terms)? What about multiplying a monomial by a trinomial? Two trinomials?

Write a statement about how many terms you will get when you multiply a polynomial with m terms by a polynomial with n terms. Give an explanation to support your statement.

Answer 1

1.To add and subtract polynomials, the horizontal technique of deleting parenthesis, collecting like terms, and simplifying is the simplest. When there are negative terms, it gets more difficult since one must ensure that the term remains negative when gathering comparable terms. The vertical approach of building up a box and adding vertically takes longer to set up, but once completed, there is a clear depiction of where all of the similar terms are.

2.Because the product of a linear factor and a quadratic factor is a cubic product, algebra tiles cannot be used to simulate the multiplication of a linear polynomial by a quadratic polynomial.

3.Distribute the first polynomial's terms to the second polynomial's terms. When multiplying two terms together, remember to multiply the coefficients (numbers) and add the exponents. However, with Integers, you multiply two integers with opposite signs.

4.Before combining like terms, there will be four terms. When a monomial is multiplied by a trinomial, the result is six. There will be nine terms in two trinomials.

Explanation:

Answer 2

1.Each method works differently the angles inside them is what matters.

2. Manipulating algebra tiles can help people solve linear equations

3.Distribute each term of the first polynomial to every term of the second polynomial. Remember that when you multiply two terms together you must multiply the coefficient (numbers) and add the exponents. But with Integers you multiply two integers with different signs

4.So you know how
A monomial is a number, a variable or a product of a number and a variable.


multiply each term in one polynomial by each term in the other polynomial

Examples:

`3x2(4x2 – 5x + 7) –6xy(4x2 – 5xy – 2y2) (3x – 4y)(5x – 2y) (4x – 5)(2x2 + 3x – 6)`