1. ALGEBRA II HONORS/GIFTED SECTION 4-4 : FACTORING QUADRATIC EXPRESSIONS@
SECTION 4-4 : FACTORING QUADRATIC EXPRESSIONS

2. First, for some
MONOMIAL : an expression that is either a number, a variable, or the product of a number and one or more variables.
EXAMPLES :
BINOMIAL : The sum (or difference) of two monomials.
EXAMPLES :

3. TRINOMIAL : The sum or difference of three monomials.
EXAMPLES :
POLYNOMIAL : meaning “many terms” can be a monomial, binomial, trinomial, or an expression with more than three terms separated by addition and/or subtraction.
EXAMPLES :

4. QUADRATIC EQUATION : An equation of degree two
QUADRATIC EQUATION : An equation of degree two. The STANDARD FORM of a quadratic equation is
ax2 + bx + c = 0.
EXAMPLES :
ROOTS or ZEROES : are the solutions of a quadratic equation.
PARABOLA : The name of the graph of a quadratic equation. Parabola functions are shaped like the letter U or an upside down U.

5. Multiply the polynomial that matches your group number.
1) (x – 8)(x – 9)
(x + 5)(x – 5)
(3x – 7)(3x + 7)
(y + 20)(y – 20)
(d + 9)2
(2c – 5)2
(7j + 9)2
(4s – 7)2
ANSWERS
x2 – 17x + 72
x2 – 25
9x2 – 49
y2 – 400
d2 + 18d + 81
4c2 – 20c + 25
49j j + 81
16s2 – 56s + 49

6. SPECIAL PRODUCT FORMULAS
(so far)
Difference of Squares a2 – b2 = (a + b)(a – b)
Square of a Sum (a + b)2 = a2 + 2ab + b2
Square of a Difference (a – b)2 = a2 – 2ab + b2
Note : (a + b) and (a – b) are called conjugates.

7. Factor completely.
8) m
11) 9r2 – 25t2
(m + 11)(m – 11)
(3r + 5t)(3r – 5t)
9) r2 + 14r + 49
12) 25p2q2 – 30pq + 9
(r + 7)2
(5pq – 3)2
10) p2 – 24p + 144
13) x2 – 9x - 5
(p – 12)2
prime

8. Factor completely.
14) x2 + 14x + 48
16) 9x2 - 56x + 12
(x + 6)(x + 8)
(x - 6)(9x - 2)
15) x2 – 7x - 30
17) 12y2 + 25y + 12
(x + 3)(x – 10)
(4y + 3)(3y + 4)

9. 18) 16x2 – 48x + 36 19) -12x2y + 27y 20) 12x3y – 2x2y2 – 2xy3
-3y(2x + 3)(2x – 3)
20) 12x3y – 2x2y2 – 2xy3
2xy(3x + y)(2x – y)

10. Now…for a little Calvin and Hobbes