Introduction to Linear Polynomials | Exercise 2.2

Question 1

Find the value of the linear polynomial 5x35x - 3 if:

(i) x=0x = 0 (ii) x=1x = -1 (iii) x=2x = 2

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Solution

We will substitute the given values of xx into the polynomial 5x35x - 3.

Step 1 — Evaluate for x = 0

Let's find the value when xx is 0. We replace xx with 0 in the polynomial.

5(0)35(0) - 3

=03= 0 - 3

3\boxed{-3}

Diagram 1

Step 2 — Evaluate for x = -1

Now, let's find the value when xx is -1. We replace xx with -1 in the polynomial.

5(1)35(-1) - 3

=53= -5 - 3

8\boxed{-8}

Diagram 2

Step 3 — Evaluate for x = 2

Finally, let's find the value when xx is 2. We replace xx with 2 in the polynomial.

5(2)35(2) - 3

=103= 10 - 3

7\boxed{7}

Diagram 3

Answer

(i) -3 (ii) -8 (iii) 7

More questions in Exercise 2.2

Q1

Find the value of the linear polynomial 5x35x - 3 if:

(i) x=0x = 0 (ii) x=1x = -1 (iii) x=2x = 2

Q2

Find the value of the quadratic polynomial 7s24s+67s^2 - 4s + 6 if:

(i) s=0s = 0 (ii) s=3s = -3 (iii) s=4s = 4

Q3

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.

Q4

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

Q5

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?

Q6

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?

Q7

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?

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