Factoring & Properties of Real Numbers

Question 1

Distributive property

Answer 1

A(2 + 3)

Question 2

Property of opposite

Answer 2

A + (-a) = 0

Question 3

Identity property of addition

Answer 3

A + 0 = A

Question 4

Substitution

Answer 4

(12+12) can be changed to 24

Question 5

Transitive

Answer 5

If a = b and b = c then a = c

Question 6

Symmetric

Answer 6

If a = b then b = a

Question 7

Reflexive

Answer 7

A = a

Question 8

Associative

Answer 8

(A+b)+c =a+(b+c)

Question 9

Commutative property

Answer 9

A+b = b+a

Question 10

Natural

Answer 10

Counting numbers whole not including zero.

Question 11

Whole numbers

Answer 11

Positive whole numbers including zero

Question 12

Integers

Answer 12

Positive, negative, whole, zero

Question 13

Irrational

Answer 13

Can’t be represented as a fraction. Can’t be repeating or terminated

Question 14

Rational number

Answer 14

Written as fraction (repeats and terminates)

Question 15

Real number

Answer 15

Not imaginary

Question 16

Factoring by grouping

Answer 16

x(x+2) + 3(x+2) = (x+3)(x+2)

Question 17

Zero product Property with factoring
x^2 + 6x = 0

Answer 17

x^2 + 6x = 0
x(x+6) = 0
x = 0 or x = -6

Question 18

Difference of two squares

Answer 18

a^2 - b^2 = (a+b)(a-b)

Question 19

Sum of Cubes

Answer 19

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Question 20

Difference of Cubes

Answer 20

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Question 21

(a + b)^2
Perfect Square trinomial (positive)

Answer 21

= a^2 + 2ab + b^2

Question 22

(a-b)^2
Perfect square trinomial (negative)

Answer 22

= a^2 - 2ab + b^2

Question 23

sum of two squares

Answer 23

a^2 + b^2 = PRIME

Question 24

Finding the middle term of ax^2 + kx + 81

Answer 24

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

Question 25

Leading coefficient is 1 (x^2 + bx + c)

Answer 25

Divide the middle term into two numbers that multiply to a * c and add up to the middle coefficient.
x^2 + 8x + 15
1 * 15 = 15
Two numbers that multiply to 15 and add up to 8 are 3 and five
(x + 5)(x +3)
FOLLOW THE SYMBOL OF THE SECOND TERM

Question 26

Why is x^2 - 18x - 81 PRIME?

Answer 26

Because the C (-81) in a perfect square trinomial can’t be negative.

Question 27

Why ix x^2 + 81 PRIME?

Answer 27

It can be rewritting as x^2 = 9^2, which is always prime because a^2 + b^2 is always prime.

Question 28

How can x^2 - 10xy + 25y^2 be simplified?

Answer 28

2(x)(5y) = 10xy, so this is a perfect square trinomial. This means that we can use the formula
(square root of x +/- square root of c)^2
The +/- symbol is determined by the second term. In this case it is being subtracted, so the simplified equation is (x - 5y)^2

Question 29

How can 81m^2 + 18m + 1 be simplified.

Answer 29

18m is 2(9m)(1) so this is a perfect square trinomial. The middle term is being added. This can be written as (9m + 1)^2

Question 30

Evaluate (10.1)^2 - 4.2 * 10.1 + (2.1)^2
Use scrap paper.

Answer 30

(10.1-2.1)^2
This is a perfect square trinomial because the middle term is equal to 2(2.1)(10.1) so this is a perfect square. The formula (square root of a +/- square root of c)^2 can be used.

Question 31

How would you go about doing (3x +1)^2?

Answer 31

(3x + 1)(3x + 1)
Don’t be lazy and distribute the exponent bc that is WRONGNGNGN

Question 32

Formula for a^2 + b^2

Answer 32

(A + b)(a - b)

Question 33

(a^3 + b^3)

Answer 33

(A + b)(a^2 - 2b + b^2)

Question 34

A cubed plus b cubed

Answer 34

(a + b)(a^2 - ab + b^2):