Factoring & Properties of Real Numbers Flashcards
Distributive property
A(2 + 3)
Property of opposite
A + (-a) = 0
Identity property of addition
A + 0 = A
Substitution
(12+12) can be changed to 24
Transitive
If a = b and b = c then a = c
Symmetric
If a = b then b = a
Reflexive
A = a
Associative
(A+b)+c =a+(b+c)
Commutative property
A+b = b+a
Natural
Counting numbers whole not including zero.
Whole numbers
Positive whole numbers including zero
Integers
Positive, negative, whole, zero
Irrational
Can’t be represented as a fraction. Can’t be repeating or terminated
Rational number
Written as fraction (repeats and terminates)
Real number
Not imaginary
Factoring by grouping
x(x+2) + 3(x+2) = (x+3)(x+2)
Zero product Property with factoring
x^2 + 6x = 0
x^2 + 6x = 0
x(x+6) = 0
x = 0 or x = -6
Difference of two squares
a^2 - b^2 = (a+b)(a-b)
Sum of Cubes
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
Difference of Cubes
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
(a + b)^2
Perfect Square trinomial (positive)
= a^2 + 2ab + b^2
(a-b)^2
Perfect square trinomial (negative)
= a^2 - 2ab + b^2
sum of two squares
a^2 + b^2 = PRIME
Finding the middle term of 16x^2 + kx + 81
The square root of a (coefficient of x^2) and c (constant) times two
16x^2 + kx + 81
2(4x)(9) = 72x so k = 72