## Exercise 6

The number of tablets sold by a shop can be modeled by the expression and price per tablet is modeled by an expression , where t is the number of months in a year. If we use this model, what is the total amount of revenue generated by the shop at the end of the year?

## Exercise 7

The area of the rectangle is given by the polynomial expression and its length given by . Find the width of the rectangle.

## Exercise 8

The distance covered by a bike is given by the expression . The time taken by the bike to covered this distance is given by the expression . Find the speed of the bike.

## Exercise 9

The number of shirts sold by the shopkeeper is given by the expression . The price per shirt is given by the expression . Find the total amount of revenue earned by the shopkeeper by selling the shirts.

## Solution of exercise Solved Polynomial Word Problems

## Solution of exercise 1

Find **a** and **b** if the polynomial is divisible by .

**Step 1**

First, find factors of the expression . Since it is a perfect square, hence it can be written as:

**Step 2**

Set the factors equal to zero:

Either or

Hence, or

**Step 3**

Put these values of in the original polynomial expression:

a) Substitute

Take on the right hand side of the equation:

b) Substitute

**Step 4**

Add both expressions together to get

Hence,

**Step 5**

Remember we got the expression in the above problem. To find the value of a, put in this expression:

Divide both sides by 2 to get the value of :

## Solution of exercise 2

Determine the value of **m** if has as one of its roots.

**Step 1**

Put in the original polynomial expression:

**Step 2**

Take 4 on the left side of the equation:

Subtract 3 from both sides of the equation to get the final answer:

## Solution of exercise 3

Find a fourth degree polynomial that is divisible by and has the roots by and .

**Step 1**

and can be written as and

**Step 2**

Multiply and together:

**Step 3**

Now, multiply with to get the fourth degree polynomial:

## Solution of exercise 4

Calculate the value of **a** for which the polynomial has the root .

Put in the polynomial expression:

## Solution of Exercise 5

Given that the length is and width is .

The area of the rectangle = length x width

=

=

=

=

Hence, the area of the rectangle is .

## Solution to exercise 6

We know that the amount of revenue generated is equal to the:

Number of items sold x Price per item

Here, Number of items sold

Price per tablet

Multiply these two expressions together:

Put in the above expression because in a year there are 12 months:

Hence, the total revenue of the shop for a year is dollars.

## Solution to exercise 7

The area of the rectangle =

Length of the rectangle =

The formula for area of the rectangle = length x width

Hence, to find the width of the rectangle, we need to divide the area by the length:

Use the polynomial long division method to solve the above expression:

The quotient is the width of the rectangle. Hence, the width of the rectangle =

## Solution to exercise 8

Since the formula for the distance is speed x time, hence we can easily derive formula of speed from this formula of distance:

speed =

Put the values in the questions in the above formula to get the speed:

speed =

Use the polynomial long division method to find the answer.

Hence, the speed of the bike is .

## Solution to exercise 9

The total amount of profit is calculated by the formula:

Profit = Price per item x Number of items sold

Hence, we will find the profit by multiplying the price of the single shirt with the total number of shirts sold.

Price of a single shirt =

Number of shirts sold =

Profit =

=

=

=

Hence, the total profit earned by the shopkeeper =

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