14 = 48 – 8a + 8 + 10 + 12

8a = 64 a = 8

a = 8

3(x4

– 3x3

+ 2x2

– 22) – (35 – 3x – x4) + 4(4x

3– 3x

2+ 3x – 2)

= 3x4

– 9x3

+ 6x2

– 66 – 35 + 3x + x4

+ 16x3

– 12x2

+ 12x – 8

= 4x4

+ 7x3

– 6x2

+ 15x – 109

Q(x) = x4

+ ax3

+ bx2

+ 8x – 9

Q(2) = 16 + 8a + 4b + 16 – 9 = -21

Q(-3) = 81 – 27a + 9b – 24 – 9 = 174

8a + 4b = -44 -27a + 9b = 126

2a + b = -11 , ( 4) -3a + b = 14 , ( 9)

a = -5

b = -1

a = -5, b = -1

a = 4, b = 60

y1 = 3x + 6

x = -2 (-2,0)

x-4 -2 2 4

y

-5

5

Q8 (i) : y – y1 = m(x – x1)

m = – 34

(x1 , y1) = (-3 , 5)

y – 5 = – 34

(x – -3)

y – 5 = – 34

x – 94

y = – 34

x + 114

4y = -3x + 11 3x + 4y – 11 = 0

Q8 (ii) : y – y1 = m(x – x1) (x1 , y1) = (-2 , 3) (x2 ,y2) = (5, – 8)

m = y2 – y1

x2 – x1

= -8 – 35 – -2

= – 117

y – 3 = – 117

(x – -2)

y – 3 = – 117

x – 227

y = – 117

x – 17

7y = -11x + 1 11x + 7y + 1 = 0

x-4 -2 2 4 6 8

y

-5

5

10

Straight line y – y1 = m(x – x1)

(x1 , y1) = (-3, 7) m = ?

-4y = – x – 5

y = 1

4 x + 5

4

m1 = -4

So y – 7 = -4(x – -3)

y – 7 = -4x – 12

y = -4x – 5

4x + y + 5 = 0

= b2

– 4ac

= (-20)2

– 4 4 25

= 400 – 400

= 0

(-3, 0) (0, – 6) (2, 0)

b = 1, c = -6 y = x2

+ x – 6

x1 2 3 4

y

- 30

- 20

- 10

10

x1 2 3 4

y

- 30

- 20

- 10

10H = 8x – 4x

2+ 5, x [0,4] ,

H = -4x2

+ 8x + 5

H = -4 x2

– 2x – 54

H = -4 (x

2– 2x + 1) – 1 – 5

4

H = -4

(x – 1)

2– 9

4

y = (x – 2)(x + 3)(2x – 1)

(x – 2)(x + 3)(2x – 1) = 0

(2,0) (-3,0)

12

,0

x = 0

f(x) = 2x3

+ x2

– 13x + 6 f(0) = 6

(0,6)

x- 5 - 4 - 3 - 2 - 1 1 2 3 4 5

y

- 10

- 5

5

10

15

20

25

96 = a (-4)2(3)(-2)

a = -1

y = – (x – 4)2(x + 3)(2x – 5)

a = 5, b = 27, c = 30, d = 256, e = 96

y = -5x4

+ 27x3

+ 30x2

– 256x + 96

0 = (-2)4

+ a (-2)3

+ b (-2)2

+ 36(-2) + 144

-8a + 4b + 88 = 0

-8a + 4b = -88

0 = (-2)4

+ (a + 3)(-2)3

– 23(-2)2

+ (b + 10)(-2) + 40

0 = -8a – 2b – 80

-8a – 2b = 80

a = -3, b = -28

a = -3, b = -28