The polynomial f(x) = 3 x^{ 4} + 5 x^{ 3} - 17 x^{ 2} - 25 x + 10

has irrational zeros at + √(5) and - √(5). Find the other zeros

1, 4

2, 2/3

2/3, 1/2

-2, 1/3

17. If (x-1) and (x+1) are both factors of the equation x³ +px +qx + 6 = , evaluate p and q, respectively

3, -4

-1, 4

1, -3

-6, -1

18. If x + 1 is a factor of x^{3} + 3x^{2} + kx + 4, find the value of k

5

6

4

3

19. Factorize the polynomial x^{ 2} + 5x + 6

(x + 2)(8)

(x + 2)(x + 6)

(x + 2)(x + 3)

(x + 5)(x + 3)

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

3

4

2

5

21. Given that ax^{4} – 2x^{3} + cx^{2} – 6x – 9 = 0. When x = -1 or 3, calculate the values a and c, respectively.

1, 0

1, 2

2, -1

0, -1

22. 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.

5, 7

2, 3

-15, -7

8, -8

23. Multiply (x + 3y + 5) by (2x² + 5y + 2)

2x³+6yx²+5xy+15y

x²+31y+18x+2x+9

2x²+6y²x+4xy+12x²+31y+18x+2x+9

2x³+6yx²+5xy+15y²+31y+10x²+2x+10

24. Find the term independent of x in

(x + 3/x)^{8}

5760

5670

56

567

25. Add the polynomials: (-x^{2} + 5 x + 2) + (6 x^{2} + x)