What is a polynomial?

A Polynomial is a question including multiple terms. A term could be a single number or variable.

Polynomial Vocabulary

• Degree:The largest exponent of all the terms ( Each term is added together ) .
• Constant: A term in the question that does not change.
• Coefficient: The number in front of a variable used to multiply with the variable.
• Leading coefficient: The first coefficient in a question.
• Binomial: A polynomial with two terms.
• Trinomial: A polynomial with three terms.
• Monomial: A polynomial with one term.

How To Use Algebra Tiles

Adding Polynomials

Adding polynomials is more like sorting then anything. To add polynomials you find same variables and add them together. Since you don’t know the value of the variable this works, if i where to say that x = 4 then this no longer works and you have to fill in all the x’s with 4’s.

Subtracting Polynomials

To subtract polynomials you have to remove brackets first. the rule’s with subtraction are easy to remember anything in the bracket after the subtraction line becomes reversed, if it was a positive number it would turn into a negative number and if it where negative it would turn positive. after you re write the question you can simplify by adding.

Multiplying Polynomials

Multiplying polynomials was also a lot simpler then i thought it would be. in the photo we have the question 4 (3x² + 2x) for this question you would multiply 4 and 3 and get 12. then you add the x² onto the end to get 12x² and for the 4 x 2x the answer would be 8x. It is pretty much the same if the number outside the bracket has a variable  for 3x²y (2xy – 3xz) each variable has a invisible ¹ , and since we are multiplying we can use the multiplication law and add the two exponents. For the 3x²y  x 2xy you can add the invisible ¹ to make the answer 6x³y and continue like that for the rest of the questions.

Dividing Polynomials

Dividing polynomials is pretty similar to multiplying polynomials in the scene that your multiplying and dividing . when you divide a polynomial you divide the bottom number with the top number. and then add the variable to the end.  for example you would divide the 4 and the 2 to get 2 then add the 4x². If there is a variable on the bottom you do the same thing as multiplication but subtract the exponents.

Connections between polynomials and past units

There is definitely a large connection between the current unit and the past units. This unit connects the most to exponents, since some variables have exponents i think if this unit was before exponents it would have been a lot more confusing.