Page 509 - Algebra 1

Example
2
Factoring when b is Negative and c is Positive Factor 6x2 - 11x + 3 completely.
SOLUTION
The first term of the trinomial, 6x2, is the product of
(6x)(x) or (3x)(2x). So, write (6x )(x ) and (3x )(2x ).
The third term of the trinomial, 3, is the product of the last terms in the binomials. List the pairs of factors that result in a product of 3. Because b is negative, both factors will be negative.
(-1)(-3) (-3)(-1)
Check each of the pairs to see which results in the middle term, -11x.
Caution
After finding the pair that appears to work, check the other possibilities. If another answer is found, double-check your work.
Possibilities
(6x - 1)(x - 3) (6x - 3)(x - 1) (3x - 1)(2x - 3) (3x - 3)(2x - 1)
Middle Term
-19x -9x
-11x ✓ -9x
So,6x2 -11x+3=(3x-1)(2x-3). Factoring when c is Negative
Factor completely.
a. 4x2+4x-3 SOLUTION
The first term of the trinomial, 4x2, is the product of (4x)(x) and (2x)(2x). So, write (4x )(x ) and (2x )(2x ).
The third term, -3, is the product of the last terms in the binomials. List the pairs of factors that result in the product -3.
(1)(-3) (-1)(3) (3)(-1) (-3)(1) Check each of the pairs to see which results in the middle term, 4x.
Example
3
494 Saxon Algebra 1
Possibilities
(4x + 1)(x - 3) (4x + 3)(x - 1) (4x - 1)(x + 3) (4x - 3)(x + 1) (2x + 1)(2x - 3) (2x+3)(2x-1)
Middle Term
-11x -x 11x x -4x
4x ✓ So,4x2 +4x-3=(2x+3)(2x-1).