Page 490 - Algebra 1

Tiling is a method for modeling the factoring of trinomials, but it is a slow method for finding the factors. Thinking about how factors are multiplied leads to a quicker method.
Binomials can be multiplied using the FOIL method. In each case, the product is a trinomial.
This procedure can be reversed to factor a trinomial into the product of two binomials. There is a pattern for factoring trinomials that are written in the standard form ax2 + bx + c; that is, when a = 1.
1. The last term of the trinomial, c, is the product of the last terms of the binomials.
2. The coefficient of the middle term, b, is the sum of the last terms of the binomials.
Factoring when c is Positive Factor each trinomial.
a. x2+9x+18 SOLUTION
In this trinomial, b is 9 and c is 18. Because b is positive, it must be the sum of two positive numbers that are factors of c.
Three pairs of positive numbers have a product of 18. (1)(18) = 18 (2)(9) = 18 (3)(6) = 18 Only one pair of these numbers has a sum of 9.
(1) + (18) = 19 (2) + (9) = 11 (3) + (6) = 9 The constant terms in the binomials are 3 and 6.
x2 +9x+18=(x+3)(x+6)
Thefactoredformof x2 +9x+18is(x+3)(x+6).
b. x2-5x+4 SOLUTION
In this trinomial, b is −5 and c is 4. Because b is negative, it must be the sum of two negative numbers that are factors of c.
Two pairs of negative numbers have a product of 4. (-1)(-4) = 4 (-2)(-2) = 4
Only one pair of these numbers has a sum of −5. (-1) + (-4) = -5 (-2) + (-2) = -4 The constant terms in the binomials are −1 and −4. x2 -5x+4=(x-1)(x-4)
Thefactoredformof x2 -5x+4is(x-1)(x-4).
Hint
FOIL stands for First, Outer, Inner, Last.
(x + a)(x + b) Inner Outer
Example
1
Caution
Pairs of numbers can have the same product but different sums.
Lesson 72 475
First
Last