Class 9 Introduction to Linear Polynomials Notes & MCQs

Class 9 Introduction to Linear Polynomials Notes & MCQs

📌 1. What is a Polynomial?

A polynomial is an algebraic expression made of:

  • Variables (like x, y)
  • Constants
  • Exponents (whole numbers only)

👉 Example: 2x + 3, x − 5, 7x + 1

📌 2. Linear Polynomial

A linear polynomial is a polynomial of degree 1.

General form:

👉 ax + b
where:

  • a, b are constants
  • a ≠ 0

Examples:

  • 3x + 2
  • x − 7
  • 5x + 0

📌 3. Degree of Polynomial

  • Highest power of variable
  • Linear polynomial → degree = 1

📌 4. Value of Polynomial

To find value, substitute x.

Example:
P(x) = 2x + 3
If x = 2 → P(2) = 2(2) + 3 = 7

📌 5. Zero of Polynomial

Value of x where polynomial becomes zero.

Example:
2x + 4 = 0 → x = −2

MCQs (50 Questions – CBSE Style)

1. Linear polynomial is of degree:
A) 0 B) 1 C) 2 D) 3
Answer: B

2. General form of linear polynomial is:
A) ax² + b
B) ax + b
C) ax³ + b
D) a + b/x
Answer: B

3. Degree of x + 5 is:
A) 0 B) 1 C) 2 D) 5
Answer: B

4. 3x − 7 is a:
A) quadratic B) linear C) cubic D) constant
Answer: B

5. Zero of polynomial means:
A) value of x making it zero
B) value of y
C) coefficient
D) constant
Answer: A

6. If P(x) = x + 3, then P(2) =
A) 4 B) 5 C) 6 D) 7
Answer: B

7. A linear polynomial has how many zeros?
A) 0 B) 1 C) 2 D) infinite
Answer: B

8. Graph of linear polynomial is:
A) circle B) parabola C) straight line D) curve
Answer: C

9. In ax + b, a must not be:
A) 1 B) 0 C) 2 D) negative
Answer: B

10. x − 7 is a polynomial of degree:
A) 0 B) 1 C) 2 D) 3
Answer: B

📝 ASSERTION–REASON (10 Questions)

  1. A: Linear polynomial has degree 1
    R: Highest power of x is 1
    👉 A
  2. A: x² + 1 is linear
    R: Degree is 2
    👉 C
  3. A: Linear polynomial graph is straight line
    R: It has degree 1
    👉 A
  4. A: Linear polynomial has two zeros
    R: It is quadratic
    👉 C
  5. A: ax + b is general form
    R: a ≠ 0
    👉 A

📊 NUMERICALS / EVALUATION

  1. P(x) = 2x + 3, x = 2 → ?
    👉 7
  2. P(x) = x − 5, x = 10 → ?
    👉 5
  3. P(x) = 3x + 1, x = 0 → ?
    👉 1
  4. Find zero of x + 6 →
    👉 −6
  5. Find zero of 2x − 4 →
    👉 2

📄 FILL IN THE BLANKS

  1. Linear polynomial is of degree ________ → 1
  2. General form is ________ → ax + b
  3. Graph of linear polynomial is ________ → straight line
  4. Zero of polynomial makes value ________ → zero
  5. a in ax + b cannot be ________ → 0