March 20, 2015
10.4 Factoring to Solve Quadratic Equations
Factor Completely Review
Factor 3x2 - 27
First check for GCF. Then, since there are 2
terms check for difference of squares.
3x2 - 27 = 3(x2 - 9)
= 3(x + 3) (x - 3)
Factor 9y2 - 58y + 49
The polynomial has 3 terms. So, check the following.
GCF : the GCF is 1
Perfect Square Trinomial: Although 9y2 = (3y)2 and 49 = 72,
58 y is not 2(3y)(7).
Trinomial with 2 binomial factors:
Are there 2 numberswhose product is 9 * 49 or 441 and
whose sum is -58? Yes, the product of -9 and -49 is 441
and their sum os -58.
9y2 - 58y + 49 = 9y2 + [-9 + (-49)]y + 49
= (9y2 - 9y) + (-49y + 49)
= 9y(y-1) + (-49)(y-1)
= (9y - 49) (y - 1)
March 20, 2015
CHALLENGE:
Find the product of all of the integers between -100 and +100.
If a x b x c = 0 then we know that either:
a=0
b=0
or
c=0
March 20, 2015
March 20, 2015
Let's try:
3x2 - 27 = 0
factor completely first
3(x - 3)(x + 3) = 0
set each factor equal to zero
3=0
x-3=0 x+3=0
solve
not true x = 3
x = -3
March 20, 2015
March 20, 2015
Let's try:
4x2 = 36
set equal to zero
4x2 - 36 = 0
factor completely
4(x - 3)(x + 3) = 0
set each factor equal to zero
4=0
solve
x-3=0 x+3=0
not true x = 3
x = -3
March 20, 2015
Let's try:
(x - 1)(x - 1) = 36
simplify
x2 - 2x + 1 = 36
set equal to zero
x2 - 2x - 35 = 0
factor completely
(x - 7)(x + 5) = 0
set each factor equal to zero
x-7=0 x+5=0
solve
not true x = 7
x = -5
March 20, 2015
Let's try:
x(5x2 + 34x) = 7x
simplify
5x3 + 34x2 = 7x
set equal to zero
5x3 + 34x2 - 7x = 0
factor completely
x(5x - 1)(x + 7) = 0
set each factor equal to zero
x =0
5x - 1 = 0
x+7=0
solve
x=0
x = 0.2
x = -7
March 20, 2015
10.4p574:1-6, 9-19, 26, 28, 29, 31, 38, 39, 43, 46