Factoring - done

Question 1

What is factorizing

Answer 1

Writing an expression as a product of its factors. It is the reverse process of expansion.

Question 2

What is a factor

Answer 2

A number that divides the given number evenly, leaving no remainder

Question 3

What should you never do when factoring

Answer 3

Expand - you will NEVER need to expand in factoring (but you can to check answers)

Question 4

What are the product sum method steps

We can use this as is with factoring quadratic (variable not higher than second power), trinomials (3 numbers)

Answer 4

1. Rearrange expression in order of highest power
2. Find the Factors of the last/constant term
3. Based on those factors, find a combination that when added together equal the middle term (the sum) (Note: if it is a variable without a visible coefficient, the coefficient is 1)
4. These factors should be used to create a binomial expression

Question 5

What are integer laws
+ x + = ?
- x - = ?
+ x - = ?
- x + = ?)

Answer 5

+ x + = +
- x - = +
+ x - = -
- x + = -

Question 6

What is a mathematic generalization that validates factoring

Answer 6

(x + a) (x + b) = x^2 + (a + b) x + (a . b)
this validates the distributive property and the process of expanding binomials.

Question 7

How do you factor with two terms

Answer 7

1. Find the GCF
2. write the gcf outside the first bracket, which you put the remaining coefficients in (Note the coefficient might be a bracket)
3. SIMPLIFY IF POSSIBLE

Question 8

What are perfect square factorization rules

Answer 8

When we have: (a+b)^2, we get: a^2 + 2ab + b^2

And when we have: (a-b)^2, we get: a^2 - 2ab + b^2

So, when we have: a^2 + 2ab + b^2, we get: (a+b)^2

When we have a^2 - 2ab + b^2, the factored form is (a-b)^2

Question 9

What are difference of squares factorization rules

Answer 9

When we have (a+b) (a-b), we get a^2 - b^2

When we have a^2 - b^2 , the factored form is (a+b) (a-b)

Notice that the last/constant term (of the the expanded form) is a perfect square. The factored form is + or - of the perfect square

Question 10

What are the steps to factor with four terms

Answer 10

Steps
1. Group to remove common factors
2. Identify the coefficients of each term, can they be made into a common bracket
3. Remove common factors to create two sets of brackets or a coefficient
4. Remove common factor created

Question 11

Difference of squares rule

Answer 11

Expansion rule:
(a+b)(a-b) = a^2 + b^2
Middle terms cancel out in expanded form
So, factored rule:
a^2 + b^2 = (a+b)(a-b)