# ALGEBRA II HONORS/GIFTED @ SECTION 4-4 : FACTORING ALGEBRA II HONORS/GIFTED @ SECTION 4-4 : FACTORING QUADRATIC EXPRESSIONS 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 : 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 : 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. Multiply the polynomial that matches your group number. ANSWERS 1) (x 8)(x 9) x2 17x + 72

2) (x + 5)(x 5) x2 25 3) (3x 7)(3x + 7) 9x2 49 4) (y + 20)(y 20) y2 400

5) (d + 9)2 d2 + 18d + 81 6) (2c 5)2 4c2 20c + 25 7) (7j + 9)2 49j2 + 126j + 81 8) (4s 7)2

16s2 56s + 49 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. Factor completely. 8) m2 - 121 (m + 11)(m 11) 9) r2 + 14r + 49 (r + 7)2 10) p2 24p + 144 (p 12)2

11) 9r2 25t2 (3r + 5t)(3r 5t) 12) 25p2q2 30pq + 9 (5pq 3)2 13) x2 9x - 5 prime Factor completely. 14) x2 + 14x + 48 (x + 6)(x + 8) 15) x2 7x - 30 (x + 3)(x 10)

16) 9x2 - 56x + 12 (x - 6)(9x - 2) 17) 12y2 + 25y + 12 (4y + 3)(3y + 4) 18) 16x2 48x + 36 4(2x 3)2 19) -12x2y + 27y -3y(2x + 3)(2x 3) 20) 12x3y 2x2y2 2xy3

2xy(3x + y)(2x y) Nowfor a little Calvin and Hobbes