Tolong dong kak jawab pake cara

1)
a. 27a – 36ab = 9a(3-4b)
b. a²+ax+ay+xy
= a(a+x) + y(a+x)
= (a+y)(a+x)
c. 15a^25 – 35a^21 + 55a^19
= 5a^19(3a^6 – 7a² + 11)
d. 4a²-2a = 2a(2a-1)
e. 25x²-36 = (5x-6)(5x+6)

2)
6x² + 7x – 3 = 0
D = 49+72 = 121
√D = 11
x1,2 = (-7±11)/12
x1 = (-7+11)/12 = ⅓
x2 = (-7-11)/12 = -3/2

6x² + 7x – 3 = 0
6x² +9x -2x – 3 = 0
3x(2x+3) -1(2x+3) = 0
(3x -1)(2x+3) = 0

6x² + 7x – 3 = 0 ( dikali 1/6)
x² + 7x/6 = 3/6
x² + 7x/6 = ½
(x + 7/6.2)² -(7/6.2)² = ½
(x + 7/12)² – 49/144 = 72/144
(x + 7/12)² = (49+72)/144
(x + 7/12) = √(121/144)
x + 7/12 = ± 11/12
x1 = 11/12 – 7/12 = 4/12 = ⅓
x2 = -11/12 – 7/12 = -18/12 = -3/2

3)
a. ( x – 2)(x + ⅔)
= (x-2)(3x+2)
= 3x² -4x -4

b. x² – (2-⅔)x + (2)(-⅔)
= x² – 4x/3 -4/3
= 3x² – 4x – 4

4)
3 – y – 10y² = 0
(3 + 5y)(1 – 2y) = 0
y1 = -3/5 → 3y1+2 = -9/5 + 10/5 = 1/5
y2 = ½ → 3y2+2 = 3/2 + 4/2 = 7/2
(y – 1/5)(y – 7/2) = 0
(5y – 1)(2y – 7) = 0
10y – 37y + 7 = 0

5)
a. 2x² – 7x + 6 = 0
D = (-7)² – 4(2)(6)
D = 49-24 = 25
D > 0
akar²nya nyata dan berlainan

b. 4x² – 2x – ¼ = 0
D = (-2)² – 4(4)(-¼)
D = 4 + 4 = 8
D > 0
akar²nya nyata dan berlainan

c. x² – 6x + 12 = 0
D = (-6)² – 4(1)(12)

D = 36-48 = -12
D < 0
akar²nya imajiner

6)
x1 + x2 = 15
x1.x2 = 54
x² – 15x + 54 = 0
D = (-15)² – 4(1)(54)
D = 225 – 216
D = 9
√D = √9 = 3
x1,2 = ( 15 ± 3)/2
x1 = (15+3)/2 = 18/2 = 9
x2 = (15-3)/2 = 12/2 = 6

1. a. 9a(3-4b)
b. a(a+x)+y(a+x)=(a+y)(a+x)
c. 5 a^19(3a^6-7a^2+11)
d. 2a(2a-1)
e. (5x+6)(5x-6)

2. 6x²+7x-3=0
pemfaktoran
(3x-1)(2x+3)=0
3x=1 maka x=1/3 atau 2x=-3 makax=-3/2
kuadrat sempurna
6x²+7x=3
x²+7/6 x=1/2
(x+7/12)²-49/144=1/2
(x+7/12)=72/144+49/144
x+7/12=√121/144=+- 11/12
x+7/12=11/12
x=4/12=1/3
atau x+7/12=-11/12 maka x=-18/12=-3/2

rumus
x=(-7+- √49-4.6.(-3))/2.6
x=(-7+- √121)/12
x=(-7+- 11)/12
x=(-7+11)/12=4/12=1/3 atau
x=(-7-11)/12=-18/12=-3/2

3. a. (x-2)(x+2/3)=0
x²-4/3x-4/3=0
atau 3x²-4x-4=0

b. x1+x2=2+(-2/3)=4/3
x1.x2=2.(-2/3)=-4/3
x²-4/3x-4/3=0
atau 3x²-4x-4=0

4. a+b=-(-1)/-10=-1/10
a.b=3/(-10)=-3/10

(3a+2)+(3b+2)=3(a+b)+4=3.(-1/10)+4=37/10
(3a+2)(3b+2)=9ab+6(a+b)+4
=9.(-3/10)+6(-1/10)+4=-7/10

10x²-37x-7=0

5. a. (-7)²-4.2.6=49-48=1
dua akar real
b. (-2)²-4.4.(-1/4)=4+4=8
dua akar real
c. (-6)²-4.1.12=36-48=-12
dua akar tidal real

6. x²-15x+54=0
x=(15+-√225-4.1.54)/2
=(15+-√9)/2
x=(15+9)/2=24/2=12
x=(15-9)/2=6/2=3