factoring polynomi;

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Name:

Factoring Polynomi;

Factoring Out the Greatest Common Monomial FirstExample 1: Factor 6x3 + 15k + 6x

+16 +10

Note: The second and th rd steps ccommon monomial.

Example 2: Factor f - 20x

You try: 3 y. 3 4

2,

Write out the polynomial.

Factor out a common monomial, an x.

Factor out a common monomial, a 3.

Factor into simplest terms.

be combined into one step by factoring out the greatest 2


Factor out the greatest common monomial

Can it be factored further?

+ 123y32 3xx

Reco nizing Special Factorin a te s

Remember the factoring patterns you already now:

e ceo wo squares: a

Perfect square trinomials: a 2 + 2ab+ (a + b) 2 and a 2 - 2ab+ (a -

There are two other factoring patterns that will prove useful:

Qx-3)Z

Difference of two cubes : ca3Äb 3 = atyab+ b2

x + qxe$l

Notice that in each of the new factoring patterns, the quadratic factor is irreducible over the integers.

Example 1: Factor the polynomial using a factoring pattern. + 64

3

3

4 q x a 12


Check to see if 1 st term is a perfect cube.

Check to see if 2 nd term is a perfect cube.

Use the sum of two cubes formula to factor.

Example 2: Factor the polynomial using a factoring pattern 8x3 - 27

33=27

3:/2.5

-343

312

721000

3

3 4

Example 3: 40k + 5x

5 g3

I3

.3



b Check to see if 2nd term is a perfect cube.

Use the difference of two cubes formula to factor.


Factor out the greatest common monomial.


Check to see if 2nd term is a perfect cube.

I + 1 s the difference of two cubes formula to factor.

2

Factor the polynomial by grouping

Example 1: xo + x2 +X+ 1


Group by common factor.

Factor.

Regroup.

Example 2: A + xo + x + 1


Group by common factor.

3 Factor.

Regroup. 4vjr--31

Apply sum of two cubes to the first term.

Substitute this into the expression and simplify.

Your Turn

Example 3' x3 +3k 3x+2

N gaJorab(0

3

factoring polynomi;

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