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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.

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