6. When the polynomial x³ + mx² + 4x + 2 is divided by x + 2. What is the value of m?

5

2

3

4

7. If

find P+ Q

41/187

51/192

24/362

61/678

8. Use Bionomial Theorem to find the first three terms in the expansion of (1 + x)^{15}

1 + 15x + 105x²

2 + 45x + 735x²

45 + 46x² +342x³

3x+ 536x³

9. Find the value of M if

5/3

-2/3

2/3

-5/3

10. Split

into partial fractions

(x + 9) - (9/2x)

x + (9/2x) + 75/2(x-2)

(x + 9) - (9/2x) + 75/2(x-2)

x + 9

11. Find the binomial expansion of (0.7)^{5}

5.8589

0.16807

108.67

45.075

12. If x^{4}-kx^{3} + 10x² + lx - 3 is divisible by (x-1) and if when it is divided by (x+2) the remainder is 27, find the constants k and l, respectively.

2, 3

5, 7

-15, -7

8, -8

13. Find the third term in the expansion of (1-2x)^{10}

123x²

180x²

12

20x

14. Find the roots of x³ + 2x² - 5x + 6 = 0

1, 3, 2

-1, 3

1, -2, -3

-1, -3, 2

15. Use the binomial theorem to expand (1 + 2x)^{5} in ascending powers of x.

Hence find the value of (1.02)^{5} correct to 4 decimal places.

1 + 10x + 40x² + 80x3 + 90x4 + 32x5, 1.10

1 + 10x + 40x² + 80x3 + 80x4 + 32x5, 1.1041

1 + 10x + 40x² + 80x4 + 32x5, 1.1

1 + 80x3 + 80x4 + 32x5, 1.1041

16. Express

in partial fractions.

4/(x+1) + 3/(x+3)

7/(x+2) - 2/(x-2)

2/(x+1) + 3/(x-2) + 2/(x+2)

4/(3x+2) + 3/(x+1) + 1/(x+3)

17. Resolve

into partial fractions.

2/(x-1) - 3/(x+1) + 2/(x+3)

2/(x-1) + 3/(x+1) + 1/(x+3)

2/(x-1) - 1/(x+1) + 1/(x+3)

2/(x-1) - 3/(x+1) + 1/(x+3)

18. When the expression pm² + qm + 1 is divided by m- 1, it has a remainder of 2 and when divided by m + 1 it has a remainder of 4. Find pq

-1

2

1

-2

19. If , the value of P is

3

1

-1

2

20. If (x-3) and (x+5) are factors of the expression x³ + mx² - nx - 45, what is the product of m and n

55

45

35

67

21. Use Bionomial Theorem to find the first three terms in the expansion of (1 - x/2)^{12}

4x - 89x

2-7x+ 13x²

7x - 536x²

1 - 6x +16.5x²

22. Express

in partial fractions

5/2(x-1) - 1/2(x+1)

x/(x+1) + 1/(x-1)

5/2(x+1) - 1/(x-1)

1/(x+1) + 4/(3-x)

23.

The graph of the polynomial y = a x^{ 4} + b x^{ 3} + c x^{ 2} + d x + e

is shown below. Find the coefficients a, b, c, d and e.

a = -18, b =4, c = 14, d = 0, e = -2

a = -1 / 7, b = 1, c = 1, d = 0, e = -4

a = -1 / 8, b = 0, c = 1, d = 0, e = -2

a = 8, b = 0, c = 1, d = 10, e = 2

24. If

find the values of the constants P and Q

P = 3, Q = 1

P = 3, Q = 2

P = 1, Q = 2

P = 2, Q = 2

25. Find the coefficient of x³ in the binomial expansion of (2-5x)^{7}