Unit 3 math quiz

Mathematical identity

A special type of equation that is true for any values of the variables

Difference of squares identity

m² - n² = (m - n) (m + n)

Identity used for perfect square trinomials

a² + 2ab + b² = (a + b)²

Sum of cubes identity

a³ + b³ = (a + b) (a² - ab + b²)

Difference of cubes identity

a³ - b³ = (a - b) (a² + ab + b²)

Mnemonic for solving difference/sum of cubes

• CRummy CRummy SOPS

• CR = Cube Root

• SOPS = Square, Opposite Products, Square

(a + b)/c = ….. for any real numbers (a, b, or c)

• a/c + b/c

• This is true for rational numbers and for polynomial expressions

What rule do we use to simplify each term when dividing by a monomial that contains a variable?

The quotient rule

The quotient rule

• When we divide with the same base, we will subtract the exponents

• a^m / aⁿ = a^m-n

What is the step by step process for dividing polynomials

1. Completely factor both the numerator and denominator

2. Identify all common factors that are present in both the numerator and denominator - these could be monomial or binomial factors

3. Divide out all common factors from the numerator and the denominator

4. Simplify the resulting expression

Polynomial

the sum or different of terms which have variables raised to non-negative integer powers and coefficient that are constant

Leading coefficient

The coefficient of the first term of a polynomial written in descending order of exponents

Degree (of a polynomial)

The largest exponent or the largest sum of exponents of a term within a polynomial

Constant term

The term which has a fixed value and no variables

Leading term

The term with the highest exponent on the variable

Product of powers law

When multiplying two exponential expressions with the same base, add the exponents