University:
Meadowvale Secondary School
Course:
Function
Academic year:

2024
Views:

170

Pages:

3
Author:

J. Anderson

(20+951-001)0( (5+20) = Ha²+20 b. 10a2-15ab + a³ c-x²y-2xy² + xyz =-xy(x+2y-z) EXAMPLE 2: DIFFERENCE OF SQUARES Two perfect squares are separated by a minus sign. a.x²-16 1 XX=x2 = (x+4)(x-4) 4.4-=-16 c. 12x²y-3xy = 3xy (4x²-1) = 3xy (2x+1)(2x-1) = 22 d. 2a(x + y)-3b(x+y) = 2ax+2ay-36x-3by 2 alx+y)=3b (x+y) = (2a-16) (x+y)x'x'= x² 2 -3.3-9 2.42= b. = (x+3y²) (x-3y²) 4 2 d. 2x-2 = 2(x1) = 2(x+1)(x12) = 2(x+1)(x²)(1) = 2(x+1)(x+1)(x+1)(x-1) 9.9=81 n²²=n4 e.x² - (3x + y)² f. 81m³n - ya = (x+1(3x+y)) (x+3x+y)) = (9m4n²+y²) (9m²²²y +) =(x+3x+y)(x-3x-y) = (9m²²+y+) (3m²+y²) (3m² - = (4x+y) (-2x-y) 1 a. x²-4x-12 b.b²+7b-18 1x12 (-6)+2=-4 2x6 1x18 9+(-2)=72x9 3x4 = (x+q)(x-2) 3x6 (x-6) (x+2) b. a18ad63d2 = (a+3d) (a-21d) d. 2p² + 52p+50 = 2 (p²+26p +25) aaa3-21-63 = 2 (pt) (+25) C pp=p² 1x25=25 2 EXAMPLE 4: TRINOMIALS TYPE II Has 'a' that is NOT '1' or zero. Use the trial and error method-faster! a. 3x²-13x+12 b. 6x²+11x+3 3.12=36 4x +-1=-13 x 1 = (3x+1) (2x+3) T 1 1x36=3x²-4x-9x +121 2x 18 3×12=(3x2=9x) (4x+12)1 4x9 6x6 = 3x(x-3) 4(x-3) = (3x-4) (x-3) 3.1=3 3.2=6 C. 8x²-2x-15 d. 16x328x230x = (4x+5) (2x-3) 4.2 = 8 5.-3=-15 EXAMPLE 5: FACTORING BY GROUPING Basically, factoring sections, that is all! a. ac + bc-ad-bd = (ac+bc) (-ad-bd) = c(+b)-d(a+b) Same = (c-d)(a+b) c.y²-x2-14x-49 = y² + (-x2-14x-49) = my²-1(x²+14x +49) =y2(x+7) 2 = (y-1))(y+(7) =(y-x-7) (y+x+7) e. km²+2mn-n² = K2 (-m²+2mn-n²) = x²- (m²-2mn+n²) = K²- (m-n)² = (K-(m-n)) (K+(m-n) = =(K-m+n) (K+m-n) =(x+1)(x()) =(x-y-z) (x+y+z) = 2x (8x2-14x-15) = 2x (4x + 3) (2x-5) ↑ 4/2=8 3.-5-15 b. 5mn+15m-2n-6 = (Smn+15m) (-2n-6) = 5m (+3) - 2 (r(+3) -2 Same = (n+3) (5m-2) d. a²-2ab+b²-m² = (a²-2ab+b²)-м² (a-b)²-m² = ((a-b)+m) ((4-6)-M) (a-b+m) (a-b-m) = = f.x2-y2-2yz-z2 = x²- (y²+2yz + z²) = x² - (y+z)² -