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Factoring the Sum and Difference of Cubes
Forumulas
Expand these formulas to show that they are correct.
Example 1 Factor: y^3  8
Example 2 Factor: z^3 + 125
Recalling the Difference of Squares Formula
Difference of Squares:
Example 3 Factor: 25x^2  81
General Rules for Factoring
1. Factor out the GCF .
2. Identify whether the polynomial has two terms , three terms, or more
than three terms.
3. If the polynomial has more than three terms, try factoring by grouping.
4. If the polynomial has three terms, check first for a perfect square
trinomial.
Otherwise, factor the trinomial with the grouping method (or the trial and error
method).
5. If the polynomial has two terms , determine if it fits the pattern for
(a) a Difference of squares, or
(b) a Difference of cubes , or
(c) A sum of cubes .
6. Be sure to factor completely.
7. Check your answer by multiplying .
Example 4 Factor: 3ac + ad  3bc  bd
Example 5 Factor: 2x^2 + 8x  8
Example 6 Factor: p^3  5p^2  4p
Steps for Factoring Trinomials by Grouping
Your trinomial has the form ax^2 + bx + c.
1. Identify a, b, and c.
2. Find m and n such that mn = ac and m + n = b.
3. Rewrite your original trinomial as ax^2 + mx + nx + c.
4. Group the first two terms and the last two terms and factor each of them.
5. Finish by factoring the common binomial from the two resulting terms.
Example 7 Factor: 7p^2  29p + 4
1. Identify a, b, and c.
2. Find m and n such that mn = ac and m + n = b.
3. Rewrite your original trinomial as ax^2 + mx + nx + c.
4. Group the first two terms and the last two terms and
factor each of
them.
5. Finish by factoring the common binomial from the two resulting terms.
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