more Algebra

Rewrite each polynomial in standard form. Then identify the leading coefficient, degree, and number of terms. Name the polynomial.

5. 4x^2-3x^3+6x+7

7. 1-11x+9x^2

Add or subtract. Write your answer in standard form.

9.(8x^3-4x^2-3x+1) - (1-5x^2+x)

11. (5x-2x^2) - (4x^2+6x-9)

Find each product.

17. 5x^2(3x-2)

19. ab^2(a^2 - a+ab)

21. (2x+5)(x^3 - x^2+1)

23. (x+4)(x^4 - 3x^2+x)

25. A cylinder has a height of x^2 - x - 3and a radius of 2x. Express the volume of the cylinder as a sum of monomials.

Divide by using long division.

27. (8x^4 + 6x^2 - 2x + 4) / (2x - 1)

Divide by using synthetic division.

29. (x^3 + 2x - 1) / (x-2)

Determine whether the given binomial is a factor of the polynomial P(x).

31. (x+3); P(x)=x^3+2x^2-5

33. (x-2); P(x)=2x^3-3x^2=x-6

Factor each expression.

35. 4x^3-8x^2-x+2

37. 16x^3-2

Identify all of the real roots of each equation.

39. x^3+6x^2+9x+2=0

41. x^4-12x^2+27=0

43. x^3-5x^2+4=0

Write the simplest polynomial function with the given roots.

45. -3,2,4

47. - square root 2, -1

49. square root of 2, square root of 3

Solve the equation by finding all roots.

51. x^3-x^2=4x-4=0

53. x^4-63/4x^2-4=0