ALGEBRA II HONORS/GIFTED SECTION 4-4 : FACTORING QUADRATIC EXPRESSIONS @ 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 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. 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 49j2 + 126j + 81 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 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

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)

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)

Now…for a little Calvin and Hobbes