Polynomials Test Review

What is anything to the power of 0?

1

Convert x^-3 into a positive power.

1/x^3

True/False: Polynomials are often referred to by the degree of their highest term.

True

True/False: You cannot factor an addition of 2 squares.

True

How can you solve these kinds of trinomial problems?

Using the x method thingy, find what adds to the middle term coefficient and what multiplies to the constant. Then since your factoring, you are able to split the x^2 into 2 binomial x's, with (x, ) and (x, ). Then after finding these 2 numbers you put them either added or subtracted by x.

What is x(x)

x^2

what is (x+y)^2

x^2+y^2

Write subtract x from y in numerical format.

y-x

What is a variable?

A letter being used to replace a number that is unknown.

What does the square of a binomial result in?

A perfect square trinomial.

What is a constant?

A single number without a variable attached to it.

What do you call a single term polynomial? Dual term? Triple Term? What do you call a polynomial that has more than three terms?

A single term is a monomial, a dual term is a binomial, a triple term is a trinomial, and you call a polynomial with more than three terms just a polynomial.

What is a Polynomial?

Combination of multiple terms separated with either an addition or subtraction sign .

How do you multiply polynomials? Include the rules for multiplying polynomials in your answer.

First you must Distribute if necessary. You should use rules like multiplying exponents with same base=add powers. Also, to multiply you must multiply the coefficients then multiply the variables by adding powers. After, once you finish your distribution, you should just combine the like terms since its literally just adding from then on. Follow addition rules.

What is the degree of a polynomial term? How is it determined? Give a few examples of this.

Highest exponent of a variable. It is determined by the power of the variable. For example, 5x^4 is a 4rth degree term

How do you subtract polynomials? State the rule for whenever doing so.

In this case, you do the same as addition but just add an extra step. You should first distribute the minus sign amongst the 2nd set of terms. Then after, you are free to add the like terms the same way you do for addition.

What is the degree of a polynomial? How is it determined? Show and example.

It is the degree of the monomial with the greatest valued exponent. An example of this is 7x^3+6x^2, and in this case this would be a 3rd degree polynomial.

If a variable doesn't appear to have an exponent attached to it, what is it to the power of?

It is to the power of 1

What is standard form and how is standard form for a polynomial arranged?

It is when a polynomial is written with the exponents in descending order. It is also arranged from the highest degree to the lowest degree.

What are like and unlike terms?

Like terms are 2 or more terms that have the same variable and the same exponent. Unlike terms are 2 or terms that have different variables and/or different exponent.

What is a Term and what separates terms?

Mathematical Expression made up of a number and a variable. Terms are separated through either an addition or subtraction sign in between them.

After factoring using GCF, what do you do if you encounter a problem like x(x^2+bx+c)

Remember the trinomial method we did before? Just do that same exact thing.

After factoring using GCF, what do you do if you encounter a problem like x(5x^3-20x?)

Since you would have a difference of 2 squares, you could just seperate the difference of 2 squares into (x+#)(x-#)

When you are given a trinomial in the form of x^2+bx+c (example: x^2+8x+12) what will the constants in its factored form add and multiply to?

They will multiply to c and add to b.

True/False: The degree of a Polynomial helps us arrange the polynomial, and it is arranged from the lowest degree to the highest.

The first part is true, but what makes it false is that it is arranged from the highest degree to the lowest.

What is a leading coefficient?

The leading coefficient is the coefficient that is connected to the variable with the highest exponent value.

What is a coefficient?

The number in front of a variable, aka the number being multiplied to a variable.

What does simplest form of a polynomial mean?

When there are no like terms left it is in simplest form.

When you have a term with more than one variable, how do you get the degree of the term? Show an example.

When you have a term with more than one variable, you get the degree of the term by adding the exponents of each variable. An example of this is 8x^3y^2, and the answer would by 5th degree.

How do you add polynomials? Addition: If you have x, what is it the same as? If you had to add it to for example, 3x, what would the result be.

You add the like terms. Like terms are terms with the same variable and the same exponent. You CAN NEVER add terms with the same variable but different exponents. If you had x, its the same as 1x. If you add it to 3x, you get 4x.

When multiplying exponents that have the same base, what do you do to the exponents?

You add them.

How can you factor using gcf? Should a gcf be the first thing you look for when trying to solve a problem?

You can factor by simplifying a polynomial that cant be simplified through the x thingy method or the difference between perfect squares method. You basically find the coefficient and the x and squarage that al 3 are divisible by. THIS SHOULD ALWAYS BE THE FIRST THING YOU DO, AS IT ALLOWS FOR YOU TO SEE THE OTHER METHODS.

How do you multiply polynomials when it is distributing a binomial (EX: (x+8)(x+7))

You distribute both values in the first expression of the binomial to the values in the 2nd expression. From then on you just add using the addition rules.

How do you multiply polynomials when you are multiplying three expressions?

You do the same as distributing a binomial, but twice. First you multiply 2 by distribution. Whatever result you get from distributing 2 you then multiply to the last term.

How do you find the dimensions of a rectangular prism if they give you the volume?

You factor it and each of the 3 terms you get after are each dimension of the rectangle.

What should you do when re-arranging a polynomial, and you see that the leading term has a negative attatched to it?

You include the negative when bringing the term back to the front.

When you raise an exponent to another power, what do you do to the exponents?

You multiply them.

Why can you not factor an addition of 2 squares with the difference of squares method?

You will end up getting something like #(x+4)(x+4) and once double distributing you actually get another trinomial instead of the binomial you get usually.