Class 8 Maths - Factorisation CBSE Worksheets

Multiple Choice Questions

Q1:The radius of a circle is 7ab – 7bc – 14a cm, then circumference of the circle is (Given π = 22/7)
(a) 22(ab -bc-2a)
(b) 44(ab -bc-2a)
(c) (ab -bc-2a)
(d) None of these

Q2: Factorised form of x² − (p − 5) x − 5p is
(a) (x-5)(x-p)
(b) (x+5)(x+p)
(c) (x-p)(x+5)
(d) (x+p)(x-5)

Q3: Factorised form of r² – 10 r + 21 is
(a) (r - 7) (r - 3)
(b) (r -7) (r +3)
(c) (r +1) (r - 4)
(d) (r -1) (r - 4)

Q4: The expression is
(a) (2x+3)
(b) (3x+2)
(c) (2x -3)
(d) (3x-2)

True and False

Q1: x² + 4x + 3 is factorized as (x+1) (x+3)

Q2: x² + (a + b) x + ab = (a + b) (x + ab)

Q3: h is a factor of 2π (h + r).

Q4: Factors of (96 − 4 x − x²) is (x+12)(8-x)

Q5: Common factor of 17 abc, 34 ab², 51a²b is 17ab

Fill in the Blanks

Q1: −x + x³ is factorised as ______

Q2:  __________

Q3: Factorised form of (x-10)(x+7) + 16 is _______

Q4: Factorised form of 23xy – 46x + 54y – 108 is _____

Q5: Factorized form of a¹² x⁴ − a⁴ x¹² is ____________

Answer the following questions

Q1: Find the common factors of the following terms.
(a) 25x²y, 30xy²
(b) 63m³n, 54mn⁴

Q2: Factorise the following expressions.
(a) 54m³n + 81m4n²
(b) 15x²y3z + 25x3y²z + 35x²y²z²

Q3: Factorise the following polynomials.
(a) 6p(p – 3) + 1 (p – 3)
(b) 14(3y – 5z)³ + 7(3y – 5z)²

Q4: Factorise the following:
(a) p²q – pr² – pq + r²
(b) x² + yz + xy + xz

Q5: Factorise the following polynomials.
(a) xy(z² + 1) + z(x² + y₂)
(b) 2axy² + 10x + 3ay² + 15

Q6: Factorise the following expressions.
(а) x2 + 4x + 8y + 4xy + 4y2
(b) 4p² + 2q² + p²q² + 8

Q7: Factorise:
(a) a² + 14a + 48
(b) m2 – 10m – 56

Q8: Factorise:
(a) x⁴ – (x – y)⁴
(b) 4x² + 9 – 12x – a² – b2 + 2ab

Q9: Factorise the following polynomials.
(a) 16x⁴ – 81
(b) (a – b)² + 4ab

Q10: Factorise:
(а) 14m5n⁴p² – 42m7n3p7 – 70m6n⁴p3
(b) 2a²(b2 – c²) + b2(2c² – 2a²) + 2c2(a² – b2)

Q11: Factorise:
(a) (x + y)² – 4xy – 9z²
(b) 25x² – 4y² + 28yz – 49z²

You can access the solutions to this worksheet here.