Quadratic Factoring

Question 1

Simple Trinomial

Answer 1

A trinomial with a leading coefficient of 1

1x²+bx+c which is the same as x²+bx+c

Question 2

Complex Trinomial

Answer 2

A trinomial with a leading coefficient other than 1

a is not 1 for ax²+bx+c

Question 3

Special Binomial

There are 3, but we have only studied 1 called…

Answer 3

Difference of Squares, i.e.,
x² - 4
9y² - 36

A perfect square minus a constant

Question 4

To factor a Simple Trinomial

When a is 1

Answer 4

Find 2 magic numbers, such that
they multiply to the constant term
and add to the x term

mn=c and m+n=b if x²+bx+c factors to (x+m)(x+n)

Question 5

To factor a Difference of Squares

A perfect square minus a constant

Answer 5

Find the root of both terms,
then write as two factors: a difference and a sum

(a²x²-b²) = (ax - b)(ax + b)

Question 6

To factor a Complex Trinomial

When a is not 1

Answer 6

Use the box method…
Column 1: 2 terms that multiply to give the leading term
Column 2: 2 numbers that multiply to give the constant term
Check: cross multiply the box and then add and compare to the x term
If the Check passes: Read your Factors from the Rows of the box

Question 7

If the Box method fails…

i.e., If cross multiplying the box and adding doesn’t equal the x term

Answer 7

1. Try swapping the order for Column 2
2. Try different numbers for Column 2
3. Try different terms for Column 1
4. Consider all possible multiples, including 1
5. Check the Discriminant

The discriminant (b² - 4ac) needs to be 0 or a perfect square to use Box

Question 8

The first step of factoring is always…

Answer 8

Check for and factor out Common Factors

Question 9

The last step of factoring is always…

Answer 9

Check each factor to ensure they can’t be further factored