# Operations with Polynomials

Solve the following questions involving fundamental operations on polynomials:

A) find p(x)+4q(x)

p(x)=3x^5+70x^3-67x^2+3

q(x)=3x^3+56x^2-19

B) Find P(-1/2)if P(x)=x^4=3x^2+2

C) If P(y)=10y^2+4

Q(y)=y^3-5y^2+3y+7

Find 3P(y)+Q(y)

D) (x^2+y^2+4z^2+2xy+4yz+4zx)+(x^2+4y^2+4z^2-4xy-8yz+4zx)

E) (3x+2y)^2

F) (x+9)(x-4)

G) Divide: (6x^3-5x^2-13x+13)divided by (2x+3)

Factor completely:

A: 16x^2+40x+25

B: 6x^2-28x+16

C: x^4+2x^3-3x-6

Solve the following problems involving applicatins of polynomials:

A: Three consecutive even integers are such that the square of the third

is 76 more than the square of the second, Find the three integers?

B: A rectangular parking lot is 50 ft longer than it is wide, Determine

the dimensions of the parking lot if it measures 250 ft diagonally?

#### Solution Preview

fundamental operations on polynomials

Solve the following questions involving fundamental operations on polynomials:

A) find p(x)+4q(x)

p(x)=3x^5+70x^3-67x^2+3

q(x)=3x^3+56x^2-19

(3x^5+70x^3-67x^2+3)+4(3x^3+56x^2-19)

(3x^5+70x^3-67x^2+3)+12x^3+224x^2-19) distribute the 4

3x^5+70x^3+12x^3-67x^2+224x^2-19 put like terms together

3x^5+82x^3+157x^2-19 combine like terms

B) Find P(-1/2)if P(x)=x^4=3x^2+2

(-1/2)^4-3(-1/2)^2+2 = 1/256 - 1/4 + 2 = 449/256 = 1 193/256

(-1/2)^4+3(-1/2)^2+2 = 1/256 + 1/4 + 2 = 577/256 = 2 65/256

not sure if the = before 3x^2 was supposed to be + ...

#### Solution Summary

There are several examples of operations with polynomials, including real-life applications.