Page 508 - Algebra 1

LESSON Factoring Trinomials: ax2 + bx + c 75
Warm Up
1. Vocabulary A is a polynomial with three terms. (53)
Factor.
2.x2 +3x-10
(72)
Simplify.
4. (4x + 5)(3x - 2)
(58)
3.x2 -x-42 (72)
5. (2x + 5)2 (60)
New Concepts Recall that a pattern is used when factoring trinomials of the form x2 + bx + c. A pair of numbers is found whose product is c and whose sum is b. When a
trinomial takes the form ax2 + bx + c, the pattern no longer works. When the leading coefficient a is not equal to 1 another pattern emerges.
Factoring when b and c are Positive Factor completely.
2x2 +7x+5
SOLUTION
Since 2x2 is the product of (2x) and (x), write (2x )(x ).
The third term of the trinomial, 5, is the product of the last terms in the binomials. List the pairs of numbers that result in a product of 5.
(1)(5) (5)(1) (-1)(-5) (-5)(-1) Because the middle term, 7x, is positive, eliminate the pairs of negative
numbers. Check each of the other pairs to see which gives you 7x.
(2x + 1)(x + 5) (2x + 5)(x + 1)
Example
1
Hint
When c is positive, the second term in both binomials will have the same sign (negative or positive) depending on the sign of b.
Online Connection www.SaxonMathResources.com
11x 7x
So, 2x2 + 7x + 5 = (2x + 5)(x + 1).
Check Use FOIL to “undo” the factoring. (2x+5)(x+1) 2x2 +2x+5x+5
= 2x2 + 7x + 5 ✓
1x 5x
+10x +2x __
Lesson 75 493