Introduction to Linear Polynomials

Can you identify the terms, variables, and coefficients of this algebraic expression: 2x² + 5xy - 3y²?

Find the degrees of the following polynomials:

Write polynomials of degrees 1, 2 and 3.

What are the coefficients of $x^{2}$ and $x^{3}$ in the polynomial $x^{4}$ - $3x^{3}$ + $6x^{2}$ - 2x + 7?

What is the coefficient of z in the polynomial $4z^{3}$ + $5z^{2}$ - 11?

What is the constant term of the polynomial $9x^{3}$ + $5x^{2}$ - 8x - 10?

Find the perimeter of squares with sides $1$ cm, $1.5$ cm, $2$ cm, $2.5$ cm and $3$ cm. What will happen to the perimeters if the sides increase by $0.5$ cm?

If a player paid ₹750, how many matches did he play?

We have learnt that to evaluate the value of an algebraic expression, we substitute a value of the variable in the given expression. Consider Example 3, where the wire is bent to form a rectangle. Here, the area of the rectangle, $10x - x^2$, is a function of $x$. Can you interpret this as an input-output process? What value does the expression take when $x = 6$ cm?

Find the value of the linear polynomial 5x - 3 if:

The present age of Salil’s mother is three times Salil’s present age. After 5 years, their ages will add up to 70 years. Find their present ages.

The difference between two positive integers is 63. The ratio of the two integers is 2:5. Find the two integers.

Ruby has 3 times as many two-rupee coins as she has five rupee-coins. If she has a total ₹88, how many coins does she have of each type?

A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?

If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?

Predict the number of squares in the next three stages of the pattern and write the sequence of numbers up to Stage 7 of the pattern.

Using the expression 2n - 1, can you find out how many tiles will be there in the 15th stage and the 26th stage of the pattern? Also, which stage will contain 21 tiles and 47 tiles?

What amount will be left on the 15th day? How many days will it take for the entire amount to be spent?

For how many km will the fare be ₹130?

A student has ₹500 in her savings bank account. She gets ₹150 every month as pocket money. How much money will she have at the end of every month from the second month onwards? Find a linear expression to represent the amount she will have in the nth month.