Page 492 - Algebra 1

b. x2 +2xy-3y2
SOLUTION
In this trinomial, b is 2y and c is -3y2.
Four pairs of positive and negative terms have a product of -3y2.
(-1)(3y2) (1)(-3y2) (-1y)(3y) (1y)(-3y) Only the pair -1y and 3y has a sum of 2y, which is the value of b. So,
x2 +2xy-3y2 =(x-y)(x+3y)
Rearranging Terms before Factoring
Factor the trinomial.
-21 - 4x + x2
SOLUTION
Write the trinomial in the standard form as x2 - 4x - 21, where b is -4 and c is -21.
Four pairs of numbers have a product of -21.
(1)(-21) (-1)(21) (3)(-7) (-3)(7)
Onlythepair3and-7hasasumof -4.So,
x2 -4x-21=(x+3)(x-7)
Evaluating Trinomials
Evaluate x2 + 5x - 14 and its factors for x = 3.
SOLUTION
In this trinomial, b is 5 and c is -14.
The number pair -2 and 7 has a sum of 5 and a product of -14. So,x2 +5x-14=(x-2)(x+7)
Nowevaluatex2 +5x-14and(x-2)(x+7)forx=3.
Example
4
Hint
The terms of a trinomial are written in standard form when the terms contain descending powers of the variable.
Example
5
Trinomial
x2 +5x-14
= (3)2 + 5(3) - 14 = 9 + 15 - 14
= 10
Factors
(x-2)(x+7) = (3 - 2)(3 + 7) = (1)(10)
= 10
The results are the same. The trinomial is equal to the product of its binomial factors.
Lesson 72 477