# Flash Cards for Factoring

Hot tips that my polynomial may be a

candidate for grouping are…

1. There is no GCF. (No factorscommon to all terms.)

2. There are 4 terms.

3. I can find a GCF if I look 2-by-2.

Priority list (steps) for factoring any

polynomial:

1. Greatest Common Factor (GCF)

2. Grouping

3. Trinomial

4. Difference of Squares

The steps for Grouping are:

1. Collect the terms into groups so that

each group has a common factor.

2. Factor out the common factor in each

group.

3. If each group now has a common

factor, factor it out. If not, regroup.

Grouping Example:

ax + bx - ay - by

= x( a + b) -y (a +b)

= ( a + b)(x - y)

Steps for factoring

ax^{2} + bx + c

1. Multiply the coefficient of the first term by

the last term.

2. Find factors of the product from step (1) that

add to the coefficient of the middle term. (If

none, then prime.)

3. Rename the middle term using the factors

from (2).

4. Factor by grouping.

5. Check by FOIL

Factor: 6x^{2} - x - 2

(Note: There isn’t enough room to show the

check on this card.)

Prod 6(-2) = -12 | Sum -1 |

2(-6) = - 12 | 2 + (-6) = -4 No. |

3(-4) = -12 | 3 + -4 = -1 Yes. |

Difference of squares.

x^{2} - y^{2} = (x + y)(x - y)

Steps for solving a Polynomial Equation by

factoring.

1. Simplify and combine like terms.

Get eqn = 0.

2. Factor the polynomial.

3. Set ea. factor = 0. (zero factor prop’ty)

4. Solve ea. eqn. from step (3).

5. Check ea. sol’n in original eqn.