OBJECTIVE 1 Factor trinomials with a coefficient of 1 for the second-
degree term. When factoring polynomials with integer coefficients, we use only
integers in the factors. For example, we can factor by finding integers m
and nsuch that
is written as
To find these integers mand n, we multiply the two binomials on the right.
FOIL
Distributive propertyComparing this result with shows that we must find integers mand n
having a sum of 5 and a product of 6.
Product of mand nis 6.Sum of mand nis 5.Since many pairs of integers have a sum of 5, it is best to begin by listing those
pairs of integers whose product is 6. Both 5 and 6 are positive, so we consider only
pairs in which both integers are positive.
x^2 + 5 x+ 6 =x^2 + 1 n+ m 2 x+ mn
x^2 + 5 x+ 6
= x^2 + 1 n+m 2 x+mn
= x^2 +nx +mx+mn
1 x+m 21 x+n 2
x^2 + 5 x+ 6 1 x+ m 21 x+ n 2.
x^2 + 5 x+ 6
368 CHAPTER 6 Factoring and Applications
OBJECTIVES Using the FOIL method, we can find the product of the binomials and.
MultiplyingSuppose instead that we are given the polynomial and want to rewrite
it as the product
FactoringRecall from Section 6.1that this process is called factoring the polynomial. Factor-
ing reverses or “undoes” multiplying.
k^2 - 2 k- 3 = 1 k- 321 k+ 12
1 k- 321 k+ 12.
k^2 - 2 k- 3
1 k- 321 k+ 12 =k^2 - 2 k- 3
k- 3 k+ 1
Factoring Trinomials
6.2
1 Factor trinomials
with a coefficient
of 1 for the second-
degree term.
2 Factor such
trinomials after
factoring out the
greatest common
factor.Sum is 5.Factors of 6 Sums of Factors
6, 1
3 , 2 3 + 2 = 56 + 1 = 7Both pairs have a product of 6, but only the pair 3 and 2 has a sum of 5. So 3 and 2
are the required integers.
factors as
Check by using the FOIL method to multiply the binomials. Make sure that the sum
of the outer and inner products produces the correct middle term.
CHECK ✓ Correct
5 x Add.2 x3 x1 x+ 321 x+ 22 =x^2 + 5 x+ 6
x^2 + 5 x+ 6 1 x+ 321 x+ 22.
http://www.ebook777.com
http://www.ebook777.com