ALGEBRA II HONORSGIFTED SECTION 4 4 FACTORING QUADRATIC

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 ax 2 + 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) x 2 – 17 x + 72 2) (x + 5)(x – 5) x 2 – 25 3) (3 x – 7)(3 x + 7) 9 x 2 – 49 4) (y + 20)(y – 20) y 2 – 400 5) (d + 9)2 d 2 + 18 d + 81 6) (2 c – 5)2 4 c 2 – 20 c + 25 7) (7 j + 9)2 49 j 2 + 126 j + 81 8) (4 s – 7)2 16 s 2 – 56 s + 49

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

Factor completely. 8) m 2 - 121 (m + 11)(m – 11) 9) r 2 + 14 r + 49 (r + 7)2 10) p 2 – 24 p + 144 (p – 12)2 11) 9 r 2 – 25 t 2 (3 r + 5 t)(3 r – 5 t) 12) 25 p 2 q 2 – 30 pq + 9 (5 pq – 3)2 13) x 2 – 9 x - 5 prime

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

18) 16 x 2 – 48 x + 36 4(2 x – 3)2 19) -12 x 2 y + 27 y -3 y(2 x + 3)(2 x – 3) 20) 12 x 3 y – 2 x 2 y 2 – 2 xy 3 2 xy(3 x + y)(2 x – y)

Now…for a little Calvin and Hobbes