Steemit learning challenge S22W5//Polynomial and rational expressions

Good day friends of steemit today I will be participating on @khursheedanwar learning challenge and below is my participation

[Canva]

Task 1

• Explain difference between polynomial and rational expressions .Provide examples of each type of system of equation and describe their general forms.

Polynomial expressions are the kind of mathematical expression that has variables which are raised to non negative interger powers combined using addition subtraction and even multiplication.

While A rational expressions is a kind of fraction where both the ratio of the denominator and numerator are polynomial expressions.

The general form of a polynomial expressions in one variable is

Example of a polynomial expressions
3x² + 2x + 1

Example 2
2x² - x - 1

The General form of a rational expression is

Example of a rational expression

3x² + 2x + 1 / 2x² - x- 3

!

• Task 2
• Explain steps used in simplifying a rational expression.Write some common factors required to be cancel out?

1 Factor the numerator and the denominator -- Identify the common factors in the numerator and the denominator. To do that use techniques like grouping using the difference of the square method or you can use factoring quadratics method

2 Cancel out common factors -- After you have factored the equation cancel out every common factors present in the numerator and the denominator.

3 Write down the simplified form of the expression.

Example

x² - 4
——
x + 2

The numerator can be factored as
x² - 4 = (x - 2)(x + 2)

The expression now becomes

(x - 2) (x + 2)
————
x + 2

Now cancel out the common factors which is x + 2 and x + 2 . Now your answer is now x - 2 .

• Task 3
• Please add these polynomial expressions 3x^2 + 2x + 1 and 2x^2 - x - 3 and share your final expression.

Combine the constant terms

• Share multiplication of polynomial expressions 2x + 3 and x - 2 with final outcome of resulting expression.

• Task 4
Scenario number 1

Suppose if there's a person named Ali have craft store and he is selling beads in x packet which have fixed cost of $5 plus $2 for each packet.Now you have to write polynomial expression for representing total cost(C)of buying for x packets of beads by considering that there's a 10% discount+Also you have for calculating total cost of Ali buys 5 packets of beads.

Ali total cost for buying beads are

1 Let x be the total cost of buying x packet
2 The fixed price for selling at the store is $5
3 Each packet cost $2

So the total cost before any discount will be expressed as

C(x) = fixed cost + cost per packet + number of packets

C(x) = $5 + $2(x)

Therefore C(x) = $5 + $2x
Now considering that there is a 10% discount we calculate the total cost after applying the discount

Now calculate cost before discount and substitute into our equation

Scenario number 2

Suppose there's a farmer harvesting x tons of wheat and 3x tons of barley.Now you need to write a rational expression for representing ratio of wheat to total harvest in which there's wheat and barley and you have to simplify expression also at end+You also need for calculating ratio of wheat to total harvest if farmer is harvesting 4 tons of wheat.

This can be represented mathematically as

So in essence both scenario explain and illustrate rational and polynomial expressions.

Thanks for reading my post I now call on @chiagoziee @anthony002 and @prince2024 to also take part in this contest