 ### written notes on factoring

SPECIAL PRODUCTS Word List -- multiplication and factoring Factor:      3x3y + 6x2 + 9x The Hardest Factoring - Monomial Factor Factor:      x2 + 6x + 5 Factoring Trinomials -- UnFOIL Sample Problems: 1 2 3 4   animation Factor:      15x2 + 11x - 12 Factoring Trinomials when the Leading Coefficient Is Not One animation ## The Hardest Factoring -- Monomial Factoring

You must end with as many terms in the parenthises as you started with in the original unfactored expression.
1st. Find the common factors.
2nd. Copy the common factors "out front" -- outside the parenthises.
3rd. Copy what's left as terms in the parenthesis.
4th. Check by multiplying.

## Factoring Trinomials - Written Instructions

Factoring Trinomials (animation) With long notes:
Factor:     x2 - 4x - 21
1st: Arrange the trinomial in descending order.
x2 - 4x - 21

x2 - 4x - 21
(x    )(x    )

3rd: List all factor pairs of the last (constant) term.
21
1 , 21
3 , 7

4th: Add or subtract to get the middle term.
21
1 , 21
+ 3 , - 7 will produce the - 4.

Since:
(+)(-) = (-)
(-)(+) = (-) produces a negative and
(+)(+) = (+)
(-)(-) = (+) produces a positive,
The - 21 is created by multiplying one negative & one positive.

This rule always works.
If the constant term is + the factors have the same sign, so ADD the factors to find the middle term.
If the constant term is - the factors have different signs, so SUBTRACT the factors to find the middle term.

In short, Check the sign of the middle (linear) term
If + , ADD to find the middle term.
If - , SUBTRACT to find the middle term.

5th: The "larger" number always takes this (linear term) sign.
x2 - 4x - 21   The - 4x is negative, so the 7 gets a negative sign.
(x + 3)(x - 7)

With short notes:
Factor:     x2 - 4x - 21
1st: Arrange the trinomial in descending order.
x2 - 4x - 21
x2 - 4x - 21
(x    )(x    )
3rd: List all factor pairs of the last (constant) term.
21
1 , 21
3 , 7

4th: Add or subtract to get the middle term.
If + , ADD to find the middle term.
If - , SUBTRACT to find the middle term.
21
1 , 21
+ 3 , - 7 will produce the - 4.

5th: The "larger" number always takes this (linear term) sign.
x2 - 4x - 21   The - 4x is negative, so the 7 gets a negative sign.
(x + 3)(x - 7)

## Factoring Trinomials when The Leading Coefficient Is Not One

Factoring Trinomials when The Leading Coefficient Is Not One (animation)          © 2005, A. Azzolino www.mathnstuff.com/math/algebra/afactor.htm