ALGEBRA: Chapter 10

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True

True/False: If one factor is a variable - It is a solution, the solution is 0.

False

True/False: If one of the factors is a constant - it is a solution.

Polynomial

An expression which is the sum of terms of the form ax^k where k is a nonnegative integer.

Degree of a polynomial

The ___ is the largest degree of its terms.

Degree

The ___ of each term of a polynomial is the exponent of the variable.

Zero product property

The ___ states that if ab = 0, then either a = 0 or b = 0 (or both).

Linear

An expression in which the highest degree is to the first power.

Quadratic

An expression in which the highest degree is to the fourth power.

Quartic

An expression in which the highest degree is to the second power.

Product of sum and a difference

(2x - 9) (2x + 9)

Square of a difference

(3x - 4)²

Square of a sum

(4x + 7)²

Cubic

An expression in which the highest degree is to the third.

FOIL

A pattern used to multiply two binomials.

Monomial

A polynomial with one term is called a ___.

Trinomial

A polynomial with three terms is called a ___.

Binomial

A polynomial with two terms is called a ___.

Constant

A term that is a number all by itself.

Constant

A term which has no variable.

Descending order

Placing of terms used in standard from greatest to least.

Standard form

Polynomials are usually written in ___ which means that the terms are placed in descending order, from largest degree to smallest degree.

Check your answer for more factoring

Remember, the last rule for factoring is ___.

Like terms

Terms that have the same variable raised to the same exponent.

(G)reatest(C)ommon(F)actor first

The first rule of factoring is ___.

Leading term

The first term in a polynomial in standard form.

(G)reatest(C)ommon(F)actor

The greatest factor that divides two numbers.

Leading coefficient

When a polynomial is written in standard form, the coefficient of the first term is the ___.

Horizontal

When adding in ___ form, add like terms.

Vertical

When adding in ___ form, you must write each expression in standard form, aligning like terms.

Add

When subtracting in vertical form, you ___ the opposite.

Product of a sum and difference

Which pattern is this: (a + b) (a - b) = a² + b² ?

Square of a sum

Which pattern is this: (a +b )² = a² + 2ab + b² ?

Square of a difference

Which pattern is this: (a - b)² = a² - 2ab + b² ?

Collect like terms

You must ___ after you FOIL as a way of simplifying your answer.


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