RBSE Class 8 Maths Important Questions Chapter 14 Factorization

Rajasthan Board RBSE Class 8 Maths Important Questions Chapter 14 Factorization Important Questions and Answers.

RBSE Class 8 Maths Chapter 14 Important Questions Factorization

Multiple Choice Questions:

Question 1.
Correct identity is:
(a) (x + a)(x + b) = x + (a - b)x² + ab
(b) (x + a)(x + b) = x² + (a + b)x² + ab
(c) (x + a)(x + b) = x² + (a - b)x - ab
(d) (x + a)(x + b) = x² + (a)x - ab
Answer:
(b) (x + a)(x + b) = x² + (a + b)x² + ab

Question 2.
Square of (2x + 3) will be:
(a) 4x² + 6x + 9
(b) 4x² + 2x + 9
(c) 4x² + 12x + 9
(d) 4x² + 9
Answer:
(c) 4x² + 12x + 9

Question 3.
Square of (6x + 1) will be:
(a) 36x² +1
(b) 36x² + 6x + 1
(c) 36x² + 6
(d) 36x² + 12x + 1
Answer:
(d) 36x² + 12x + 1

Question 4.
Product of (2a - 3) (2a + 3) is:
(a) 4a² + 2a + 9
(b) 4a² - 9
(c) 4a² - 6
(d) 4a² - 4a + 9
Answer:
(b) 4a² - 9

Question 5.
Common factor of 6x + 18xy is:
(a) y
(b) 6y
(c) 6x
(d) xy
Answer:
(c) 6x

Question 6.
Factorisation of 2x³ + x² + 2x + 1 is:
(a) (2x +1)(x² + 1)
(b) (x² + 2)(x + 1)
(c) (x + 2)(x² + 1)
(d) (x² + 1)(x +1)
Answer:
(a) (2x +1)(x² + 1)

Question 7.
Factorisation of 4x² + 8xy + 4y² is:
(a) (2x + 2y)²
(b) (2x - 2y)²
(c) (2x + y)²
(d) (x + 2y)²
Answer:
(a) (2x + 2y)²

Question 8.
Correct value of x² - y² is:
(a) (x + y)(x² + y²)
(b) (x + y)(x - y)
(c) (x - y)(x² - y²)
(d) (x - y)(x - y)
Answer:
(b) (x + y)(x - y)

Fill in the blanks:

Question 1.
Equation, which is true for all values of variables is called ___________
Answer:
identity

Question 2.
(x + a) (x + b) = x² + (______)x + (______)
Answer:
(a + b), ab

Question 3.
a² - b² = (______ ) × (a - b)
Answer:
(a + b)

Question 4.
(x - 1) (x + 1) = ___________
Answer:
x² - 1.

Very Short Answer Type Questions:

Question 1.
Find the value of 2x(2x² + 2x - 9).
Answer:
2x (2x² + 2x - 9)
= 2x x 2x² + 2x x 2x - 2x x 9
= 4x³ + 4x² - 18x

Question 2.
Simplify (x + 2) (x + 3).
Answer:
(x + 2) (x + 3)
= x² + (2 + 3)x + 2 × 3
= x² + 5x + 6

Question 3.
Factorise (2x + a) and (2x - a).
Answer:
(2x + a) (2x - a)
= (2x)² - (a)²
= 4x² - a²

Question 4.
If x² + \(\frac{1}{x^{2}}\) = 62 then find (x + \(\frac{1}{x}\)).
Answer:
x² + \(\frac{1}{x^{2}}\)} = 62
(adding 2 on both sides)
(x + \(\frac{1}{x}\))² = 64
(x + \(\frac{1}{x}\)) = \sqrt{64}
(x + \(\frac{1}{x}\)) = 8

Question 5.
If x + y = 20, xy = 34 then find x² + y².
Answer:
(x + y)² = x² + 2xy + y²
(20)² = (x² + y²) + 2 × 34
400 = x² + y² + 68
x² + y² = 400 - 68 = 332

Question 6.
Factorise 2(x + y) + 3(x + y) + 5(x + y).
Answer:
2(x + y) + 3(x + y) + 5(x + y)
= (x + y) (2 + 3 + 5)
= 10 (x + y)

Question 7.
Factorise 3x³ + 3x² + x + 1.
Answer:
3x³ + 3x² + x + 1
= 3x² (x + 1) + 1 (x + 1)
= (3x² + 1) (x + 1)