# Dividing Polynomials

1) Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) · Q(x) + R(x).

P(x) = 3x^2 + 4x â?' 1, D(x) = x + 5

P(x) =(x+5)(_____)+______

2) Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) · Q(x) + R(x).

P(x) = x^3 + 9x^2 â?' 4x + 4, D(x) = x â?' 3

P(x)=(x-3)(____)+____

3) Find the quotient and remainder using long division.

3x^4 â?' 5x^3 â?' 19x â?' 6/x^2 + x + 3

4) Find the quotient and remainder using long division.

9x^2 â?' x + 4/3x^2 â?' 9x

5)Find the quotient and remainder using synthetic division.

x^5+4x^3-12/x-1

6)Find the quotient and remainder using synthetic division.

x^4 â?' x^3 + x^2 â?' x + 2/x-3

7)Find the quotient and remainder using synthetic division.

x^3 + 5x^2 + 7x + 2/x+5

8) Find the quotient and remainder using long division.

x^6 â?' 5x^4 + 4x^2 â?' 20/x^2 â?' 5

https://brainmass.com/math/number-theory/dividing-polynomials-345475

#### Solution Summary

Polynomial division is depicted.

Factoring Polynomials (28 problems)

Find the greatest common factor for each group of monomials.

1.) 16x^2z, 40xz^2, 72z^3

Factor out the GCF in each expression.

2.) 15x^2y^2 - 9xy^2 + 6x^2y

Factor out the GCF in each expression.

3.) a (a+1) -3 (a+1)

Factor each polynomial.

4.) 9a^2 - 64b^2

Factor each polynomial completely.

5.) x^3y + 2x^2y^2 + xy^3

Use grouping to factor each polynomial completely.

6.) x^3+ax+3a+3x^2

Factor each polynomial. If the polynomial is prime, say so.

7.) 18z+45+z^2

Factor each polynomial.

8.) h^2 - 9hs + 9s^2

Factor each polynomial completely.

9.) 3x^3y^2 - 3x^2y^2 + 3xy^2

Factor each trinomial using the ac method.

10.) 2x^2+11x+5

11.) 21x^2+2x-3

12.) 8x^2-10x-3

Factor each polynomial completely.

13.) a^2b+2ab-15b

Factor each polynomial completely.

14.) m^4 - n^4

Factor each polynomial completely. If a polynomial is prime,

say so.

15.) 3x^3 - 12x

16.) 8b^2+24b+18

17.) 3x^2-18x-48

18.) 9x^2 + 4y^2

Solve by factoring.

19.) 2h^2-h-3=0

Solve each equation.

20.) 2w(4w+1)=1

Solve each equation.

21.) x^2-36=0

22.) x^3=4x

23.) (x-3)^2 + (x+2)^2=17

24.)Avoiding a collision. A car is traveling on a road that

is perpendicular to a railroad track. When the car is

30 meters from the crossing, the car's new collision

detector warns the driver that there is a train 50 meters

from the car and heading toward the same crossing. How

far is the train from the crossing?

25.)Winter wheat. While finding the amount of seed needed

to plant his three square wheat fields, Hank observed that

the side of one field was 1 kilometer longer than the side

of the smallest field and that the side of the largest field

was 3 kilometers longer than the side of the smallest field.

If the total area of the three fields is 38 square kilometers,

then what is the area of each field?

26.)Venture capital. Henry invested $12,000 in a new

restaurant. When the restaurant was sold two years

later, he received $27,000. Find his average annual

return by solving the equation 12,000(1+r)^2 =

27,000.

Bonus Problems

27.)Rectangular stage. One side of a rectangular stage is

2 meters longer than the other. If the diagonal is 10 meters,

then what are the lengths of the sides?

28.)Throwing a wrench. An angry construction worker throws

his wrench downward from a height of 128 feet with an

initial velocity of 32 feet per second. The height of the

wrench above the ground after t seconds is given

by s(t)= -16t^2 - 32t + 128.

a) What is the height of the wrench after 1 second?

b) How long does it take for the wrench to reach the

ground?