Q 1 – The common factor of x²y² and x³y³ is
(a) x²y²
(b) x³y³
(c) x²y³
(d) x³y².
Q 2 – The common factor of 14a2b and 35a4b² is
(a) a4b²
(b) 35a4b²
(c) 14a²b
(d) 7a²b.
Q 3 – The common factor of 6a3b4c2, 21a2b and 15a3 is
(a) 3a2
(b) 3a3
(c) 6a3
(d) 6a2
Q 4 – The common factor of 3a2b4c2, 12b2c4 and 15a3b4c4 is
(a) b4c4
(b) 3b2c2
(c) 15b2c4
(d) 12b2c4
Q 5 – The factorisation of 12a2b + 15ab2 is
(a) 3ab (4a + 5b)
(b) 3a2b (4a + 5b)
(c) 3ab2 (4a + 5b)
(d) 3a2b2 (4a + 5b).
Q 6 – The factorisation of 6x + 12y is
(a) 6(x + 2y)
(b) 3(x + 4y)
(c) 2(3x + 12y)
(d) none of these.
Q 7 – The factorisation of x2yz + xy2z + xyz2 is
(a) xyz(x + y + z)
(b) x2yz(x + y + z)
(c) xy2z(x + y + z)
(d) xyz2(x + y + z)
Q 8 – The factorisation of
a (x + y + z) + b(x + y + z) + c(x + y + z) is
(a) (a + b + c)(x + y + z)
(b) (ab + bc + ca)(x + y + z)
(c) (xy + yz + zx)(a + b + c)
(d) none of these.
Q 9 – The factorisation of 4y2 – 12y + 9 is
(a) (2y + 3)2
(b) (2y – 3)2
(c) (3y + 2)2
(d) (3y – 2)2
Q 10 – The factorisation of z2 – 4z – 12 is
(a) (z + 6)(z + 2)
(b) (z – 6)(z – 2)
(c) (z – 6)(z + 2)
(d) (z + 6)(z – 2).
Q 11 – The factorisation of (l + m)2 – 4lm is
(a) (l – m)2
(b) (l + m – 2)2
(c) (l + m + 2)2
(d) none of these.
Q 12 – The factorisation of
1 + p + q + r + pq + qr + pr + pqr is
(a) (1 + p)(1 + q)(1 + r)
(b) (1 – p)(1 – q)(1 – r)
(c) (1 – p)(1 – q)(1 + r)
(d) (1 + p)(1 – q)(1 – r).
Q 13 – The value of 992 is
(a) (90)2 + 2(90)(9) + (9)2
(b) (90)2 – 2(90)(9) + (9)2
(c) (90)2 + (9)2
(d) none of these.
Q 14 – The factorisation of x2 – 9 is
(a) (x – 3)2
(b) (x + 3)2
(c) (x + 3)(x – 3)
(d) none of these.
Q 15 – The value of (0.68)2 – (0.32)2 is
(a) -1
(b) 0
(c) 1
(d) 0.36.
Q 16 – The factorisation of 6x2 – 5x – 6 is
(a) (2x – 3)(3x + 2)
(b) (2x + 3)(3x + 2)
(c) (2x – 3)(3x – 2)
(d) (2x + 3)(3x – 2).
Q 17 – The value of 3.5 × 3.5 – 2.5 × 2.5 is
(a) -6
(b) 6
(c) 60
(d) 1.
Q 18 – If x = 2, y = – 1 then the value of x² + 4xy + 4y² is
(a) 0
(b) 1
(c) -1
(d) 2
Q 19 – The quotient of 12a8b8 ÷ ( – a6b6) is
(a) 3a2b2
(6) 3a2b
(c) 3ab2
(d) –3a2b2
Q 20 – On factorising 14pq + 35pqr, we get:
(a) pq(14 + 35r)
(b) p(14q + 35qr)
(c) q(14p + 35pr)
(d) 7pq(2 + 5r)
Q 21 – The factors of x2 + xy + 8x + 8y are:
(a) (x +y) (x + 8)
(b) (2x + y) (x + 8)
(c) (x + 2y) (x + 8)
(d) (x + y) (2x + 8)
Q 22 – The factors of m2 – 256 are:
(a) (m + 4)2
(b) (m – 4)2
(c) (m – 4) (m + 4)
(d) None of the above
Q 23 – Find the common factors of the following terms.
(a) 25x2y, 30xy2
(b) 63m3n, 54mn4
Q 24 – Factorise the following expressions.
(a) 54m3n + 81m4n2
(b) 15x2y3z + 25x3y2z + 35x2y2z2
Q 25 – Factorise the following expressions.
(а) x2 + 4x + 8y + 4xy + 4y2
(b) 4p2 + 2q2 + p2q2 + 8
Q 26 – Factorise:
(a) a2 + 14a + 48
(b) m2 – 10m – 56
Q 27 – Factorise:
(a) x4 – (x – y)4
(b) 4x2 + 9 – 12x – a2 – b2 + 2ab
Q 28 – Factorise:
(а) 14m5n4p2 – 42m7n3p7 – 70m6n4p3
(b) 2a2(b2 – c2) + b2(2c2 – 2a2) + 2c2(a2 – b2)
Q 29 – Factorise:
(a) (x + y)2 – 4xy – 9z2
(b) 25x2 – 4y2 + 28yz – 49z2
Q 30 – Evaluate the following divisions:
(a) (3b – 6a) ÷ (30a – 15b)
(b) (4x2 – 100) ÷ 6(x + 5)
Q 31 – Simplify the following expressions:
Q 32 – Factorise the given expressions and divide that as indicated.
(a) 39n3(50n2 – 98 ) ÷ 26n2(5n – 7)
(b) 44(p4 – 5p3 – 24p2) ÷ 11p(p – 8)
Q 33 – If one of the factors of (5x2 + 70x – 160) is (x – 2). Find the other factor.
