CBSE Questions for Class 8 Maths Factorisation Quiz 5 - MCQExams.com

Factorisation of the expression $$\displaystyle { x }^{ 4 }yz+x{ y }^{ 4 }z+xy{ z }^{ 4 }$$ results in:
  • $$\displaystyle xyz\left( { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 } \right) $$
  • $$\displaystyle xyz\left( { x }^{ 3 }+{ y }^{ 3 }+{ z }^{ 3 } \right) $$
  • $$\displaystyle { x }^{ 3 }{ y }^{ 3 }{ z }^{ 3 }\left( x+y+z \right) $$
  • $$\displaystyle { x }^{ 2 }{ y }^{ 2 }{ z }^{ 2 }\left( { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 } \right) $$
Factorise : $$\displaystyle 12{ x }^{ 2 }-24{ y }^{ 2 }+36{ z }^{ 2 }$$
  • $$\displaystyle 12{ x }^{ 2 }-2{ y }^{ 2 }+3{ z }^{ 2 }$$
  • $$\displaystyle 12\left( { x }^{ 2 }-2{ y }^{ 2 }+3{ z }^{ 2 } \right) $$
  • $$\displaystyle 12\left( { x }^{ 2 }-{ y }^{ 2 }+{ z }^{ 2 } \right) $$
  • $$\displaystyle 12\left( { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 } \right) $$
Factorisation of the expression : $$\displaystyle 7{ a }^{ 2 }-49{ b }^{ 2 }$$
  • $$\displaystyle 7\left( { a }^{ 2 }-7{ b }^{ 2 } \right) $$
  • $$\displaystyle 7{ a }^{ 2 }-7{ b }^{ 2 }$$
  • $$\displaystyle 7\left( { a }^{ 2 }-{ b }^{ 2 } \right) $$
  • $$\displaystyle 7\left( 7{ a }^{ 2 }-{ b }^{ 2 } \right) $$
Factorise: $$\displaystyle 80{ p }^{ 2 }-72p$$
  • $$\displaystyle 8p(5p-9)$$
  • $$\displaystyle 16p(5p-4)$$
  • $$\displaystyle 8p(10p-8)$$
  • $$\displaystyle 8p(10p-9)$$
Factorisation of the expression $$\displaystyle 17{ p }^{ 2 }q-102p{ q }^{ 2 }$$ results in:
  • $$\displaystyle 17pq(p-8q)$$
  • $$\displaystyle 17pq(p-q)$$
  • $$\displaystyle 17pq(p-4q)$$
  • $$\displaystyle 17pq(p-6q)$$
The factorisation of $$ \left (21a^2+3a \right )$$ is
  • $$3a(7a+1)$$
  • $$7a(3a+1)$$
  • $$3a(7a+3a)$$
  • $$3a(a+7)$$
Multiplying factors is an example of
  • polynomial
  • quadratic equation
  • division algorithm
  • factorisation
$$\left( 14{ x }^{ 2 }yz-28{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 3 }+32{ y }^{ 2 }{ z }^{ 2 } \right) \div \left( -4xy \right) $$ is equal to
  • $$\dfrac { 7 }{ 2 } yz+7xy{ z }^{ 2 }+8xyz$$
  • $$-\dfrac { 7 }{ 2 } xz+7xy{ z }^{ 3 }-\dfrac { 8y{ z }^{ 2 } }{ x } $$
  • $$-\dfrac { 7 }{ 2 } xz-7xy{ z }^{ 3 }+\dfrac { 8y{ z }^{ 2 } }{ x } $$
  • $$\dfrac { 7 }{ 2 } xz-7xy{ z }^{ 2 }-\dfrac { 8y{ z }^{ 2 } }{ x } $$
$$4a + 12b$$ is equal to
  • $$4a$$
  • $$12b$$
  • $$4(a+3b)$$
  • $$3a$$
$$(3x^2 - 2x) \div x$$
  • $$3x$$
  • $$3x - 2$$
  • $$3x + 2$$
  • None
$$(5a^3 b - 7ab^3) \div ab$$
  • $$5a^2 - 7b^2$$
  • $$5a - 7b^2$$
  • $$5a^2 - b^2$$
  • None
$$(4l^5 - 6l^4 + 8l^3) \div 2l^2$$
  • $$(2l^2 - 3l + 4)$$
  • $$l(2l^2 - 3l + 4)$$
  • $$l(2l^2 - 3l + 3)$$
  • None
Factorize $$5xyz^2-3zy$$
  • $$yz(5xz-3)$$
  • $$yz(5yz-3)$$
  • $$xz(5xz-3y)$$
  • None of these
$$15(a^3 b^2 c^2 - a^2 b^3 c^2 + a^2b^2c^3) \div 3abc$$
  • $$abc(a - b + c)$$
  • $$5abc(a + b + c)$$
  • $$5abc(a - b + c)$$
  • None
$$(3p^3 - 9p^2q - 6pq^2) \div (-3p)$$
  • $$(2q^2 + 3pq + p^2)$$
  • $$(2q^2 + pq - p^2)$$
  • $$(2q^2 + 3pq - p^2)$$
  • None
Divide the given polynomial by the given monomial:

$$\left(\dfrac{2}{3} a^2 b^2 c^2 + \dfrac{4}{3} ab^2 c^2 \right ) \div \dfrac{1}{2} abc$$
  • $$\dfrac{4}{3} (abc + bc)$$
  • $$\dfrac{2}{3} (abc + 2bc)$$
  • $$\dfrac{4}{3} (abc + 2bc)$$
  • None
$$(25x^5 - 15x^4) \div 5x^3$$
  • $$x(5x + 3)$$
  • $$(5x - 3)$$
  • $$x(5x - 3)$$
  • None
Factorize the following expression
$$16x + 64x^2 y$$
  • $$16x (1 + 4xy)$$
  • $$6x (1 + 4xy)$$
  • $$16x (1 - 4xy)$$
  • None of these
Factorize the following
$$pq - pr - 3ps$$
  • $$p(q + r - 3s)$$
  • $$p(q + r + 3s)$$
  • $$q(q + r - 3s)$$
  • None of these
Factorise the expression:
$$2a^3 - 3a^2 b + 2a^2 c$$
  • $$a^2 (2a - 3b + 2c)$$
  • $$a^2 (2a + 3b + 2c)$$
  • $$a^2 (2a - 3b - 2c)$$
  • None of these
Factorize the following expression:
$$10x^3 - 25 x^4 y$$
  • $$5x^3 (2 - 5xy)$$
  • $$5x^3 (2 + 5xy)$$
  • $$x^3 (2 - 5xy)$$
  • None of these
Find the quotient and remainder of the given expression,
$$(3x^3+4x^2-5)\div (3x+1)$$
  • $$x^2+x-\dfrac{1}{3}, -\dfrac{14}{3}$$
  • $$x^2-3x+\dfrac{5}{9}, \dfrac{14}{3}$$
  • $$x^2+3x+\dfrac{5}{9}, -\dfrac{14}{3}$$
  • None of these
The quotient when $$x^3-5x^2+7x-4$$ is divided by $$x-1$$ is.
  • $$x^2+4x+3$$
  • $$x^2-4x+3$$
  • $$x^2-4x-3$$
  • $$x^2+4x-3$$
Find the quotient and remainder of the given expression, $$(3x^3+2x^2+7x-5)\div (x+3)$$
  • $$3x^2-7x+28, -89$$
  • $$3x^2-7x+40, 125$$
  • $$3x^2-11x+40, -15$$
  • None of these
Find the quotient and remainder of the given expression, $$(2x^4-7x^3-13x^2+63x-48)\div (2x-1)$$
  • $$x^3-3x^2-8x+\dfrac{55}{2}, -\dfrac{41}{2}$$
  • $$x^3-3x^2-8x+\dfrac{55}{2}, \dfrac{41}{2}$$
  • $$x^3+3x^2-8x+\dfrac{55}{2}, -\dfrac{41}{2}$$
  • None of these
Find the quotient and remainder of the given expression,
$$(8x^4-2x^2+6x-5)\div (4x+1)$$
  • $$2x^3-\dfrac{x^2}{2}-\dfrac{3}{8}x+\dfrac{51}{32}, -\dfrac{211}{32}$$
  • $$2x^3-\dfrac{x^2}{2}-\dfrac{3}{8}x+\dfrac{51}{32}, \dfrac{211}{32}$$
  • $$2x^3+\dfrac{x^2}{2}-\dfrac{3}{8}x+\dfrac{51}{32}, -\dfrac{211}{32}$$
  • None of these
The factorized form of $$3x — 24$$ is
  • $$ 3x \times 24 $$
  • $$ 3(x - 8) $$
  • $$ 24 (x - 3)$$
  • $$ 3(x - 12)$$
Factorised form of $$23xy - 46x + 54y - 108$$ is
  • $$ (23x + 54) (y - 2)$$
  • $$ (23x + 54y) (y - 2)$$
  • $$ (23xy + 54y) (- 46x - 108)$$
  • $$ (23x + 54) (y + 2)$$
State whether the statement is true (T) or false (F).
Factorization of  $$-3a^{2} + 3ab + 3ac$$ is $$3a(-a-b-c)$$.
  • True
  • False
State whether the statement is true (T) or false (F).
Common factor of $$12a^{2}b^{2} + 4ab^{2} - 32$$ is $$4$$.
  • True
  • False
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