**Unformatted text preview: **Factoring
Factoring is the opposite of
multiplying Factor a monomial from a
polynomial 1. Determine the GCF of all terms in the
polynomial
2. Write each term as the product of the
GCF and another factor.
3. Use the distributive property to factor out
the GCF. Examples Factor out the greatest common
factor in the expression .
2 12 x 4 x 8 GCF Factor out the GCF
4 9 5 60 x 6 x 18 x y 2 To factor four terms by
grouping 1. Arrange the four terms into
two groups of two terms each.
Each group of two terms must
have a GCF.
2. Factor the GCF from each
group of two terms.
3. If the two terms formed in
step 2 have a GCF, factor it out. Factor by grouping 2 5 x xy 20 xy 4 y 2 Factor by grouping
2 12 x 8 xy 15 xy 10 y 2 Factor by grouping
3 2 5a 15a 10a 30 Factoring trinomials- part 1 To factor trinomials of the form 2 x bx c 1. find two numbers whose
product is c and whose sum is
b.
2. the factors of the trinomial will
be (x + 1st number)(x+2nd
number) Examples We need factors of 30 whose
sum is -17 2 x 17 x 30 Example 2 2 x 6 x 91 Example 3 2 x 34 x 64 Factoring trinomials –part 2 To factor trinomials of the form 2 ax bx c Using trial and error:
1. write all pairs of factors of the
coefficient of the squared term, a.
2. Write all pairs of factors of the
constant, c.
3. Try various combinations of these
factors until the correct middle term,
bx, is found. examples 2 3 x 11 x 20 Example 2 2 4a 43a 30 More examples 2 6c 11c 10 ...

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