OBJECTIVE 3 Factor trinomials.Take the following into consideration.
SECTION 6.4 A General Approach to Factoring 341
Factoring a TrinomialFor a trinomial(three terms), decide whether it is a perfect square trinomial of
either of these forms.
or
If not, use the methods of Section 6.2.
x^2 2 xyy^2 1 xy 22 x^2 2 xyy^2 1 xy 22
Factoring TrinomialsFactor each trinomial.
(a)
Perfect square trinomial(b)
Perfect square trinomial(c)
The numbers and 1 have a product
of and a sum of(d)
Use either method from Section 6.2.(e)
Factor out the common factor.= 217 z+ 5212 z- 12 Factor the trinomial.
= 2114 z^2 + 3 z- 52
28 z^2 + 6 z- 10
= 12 k+ 321 k- 22
2 k^2 - k- 6
- 6 - 5.
= 1 y- 621 y+ 12 - 6
y^2 - 5 y- 6
= 17 z- 322
49 z^2 - 42 z+ 9
= 1 p+ 522
p^2 + 10 p+ 25
NOW TRY EXAMPLE 3
EXERCISE 3
Factor each trinomial.
(a)
(b)
(c) 12 m^2 + 5 m- 28
7 x^2 - 7 xy- 84 y^225 x^2 - 90 x+ 81NOW TRY ANSWERS
- (a)
(b)
(c) 14 m+ 7213 m- 42
71 x+ 3 y 21 x- 4 y 215 x- 922Remember the
common factor.
NOW TRYOBJECTIVE 4 Factor polynomials of more than three terms.Consider
factoring by grouping in this case.
Factoring Polynomials with More Than Three TermsFactor each polynomial.
(a)
Group the terms.
Factor each group.
is a common factor.(b)
Factor each group.
is a common factor.= 15 k+ 1212 k+ 3212 k- 32 Difference of squares
= 15 k+ 1214 k^2 - 92 5 k+ 1
= 4 k^215 k+ 12 - 915 k+ 12
= 120 k^3 + 4 k^22 - 145 k+ 92
20 k^3 + 4 k^2 - 45 k- 9
= 1 x- y 21 y^2 +x^22 x-y
=y^21 x-y 2 +x^21 x-y 2
= 1 xy^2 - y^32 + 1 x^3 - x^2 y 2
xy^2 - y^3 + x^3 - x^2 y
EXAMPLE 4
Be careful with signs.