1. ALGEBRA II HONORS/GIFTED - SECTION 5-3 (Solving Polynomial Equations)@
SECTION 5-3 : SOLVING POLYNOMIAL EQUATIONS

2. ALGEBRA II HONORS/GIFTED - SECTION 5-3 (Solving Polynomial Equations)
FIVE SPECIAL PRODUCT FORMULAS
SQUARE OF A SUM (x + y)2 = x2 + 2xy + y2
SQUARE OF A DIFFERENCE (x – y)2 = x2 – 2xy + y2
DIFFERENCE OF SQUARES (x + y)(x – y) = x2 – y2
SUM OF CUBES (x + y)(x2 – xy + y2) = x3 + y3
DIFFERENCE OF CUBES
(x – y)(x2 + xy + y2) = x3 – y3
Signs for cubes – remember to use:

3. 1) Factor.
a) x3 + 4x2 + 3x + 12
What is different about this problem?
SOLUTION :
x2(x + 4) + 3(x + 4)
(x + 4)(x2 + 3)
This is called factoring by grouping.
b) x3 – 4x2 – 9x + 36
ANSWER : (x – 4)(x + 3)(x – 3)

4. 2) Find the real and imaginary solutions of each equation by factoring.
a) 6x3 + 15x2 + 9x = 0
ANSWER : 0, -1, -3/2
b) 8x2 + 10x – 3 = 0
ANSWER : ¼, -3/2
c) 2x3 – 2x2 + 3x – 3 = 0
ANSWER :

5. d) 2x3 = -54 e) x3 + 8x = 8x + 8 f) x4 = 16 ANSWER : ANSWER :
ANSWER : 2, -2, 2i, -2i

6. 3) Find the real solutions of each equation by graphing
3) Find the real solutions of each equation by graphing. Use the ZERO function of your calculator. Round to 2 decimal places.
a) 2x3 + 5 = 3x2 – 2x
ANSWER : -0.84
b) x3 – 4x2 – x + 5 = 0
ANSWER : -1.09, 1.16, 3.93

7. Q : How does a ghost solve a quadratic equation?
A : By completing the scare.
Q : What is a smart bird’s favorite math?
A : owl-gebra