Page 162 - ICSE Math 8

AT A GLANCE

¾ When an algebraic expression is a product of two or more expressions, then each of these expressions is
called factor of the given expression.

¾ The process of writing the algebraic expression as a product of its factors is called factorization.
¾ The HCF of two or more monomials is the product of the greatest common factors of the numerical
coefficients and the common variables with the smallest powers.

¾ In factorization by taking out common monomial each term of an algebraic expression is expressed as a
product of HCF of its terms and the quotient obtained when the given expression is divided by the HCF
of its terms.
¾ When a binomial is a common factor, the given algebraic expression can be expressed as the product
of this binomial and the quotient obtained by dividing the given algebraic expression by this binomial.
¾ If the given algebraic expression is expressed as the difference of two squares, then it can be factorized
2
2
by using the identity p – q = (p + q)(p – q).
¾ If the given algebraic expression is a complete square, it can be factorized by using the identities
2
2
2
2
2
2
p + 2pq + q = (p + q) = (p + q)(p + q) and p – 2pq + q = (p – q) = (p – q)(p – q)
2
¾ A quadratic polynomial can be factorized by using x + (a + b)x + ab = (x + a)(x + b).
MENTAL MATHS
1. Choose the correct option.

2
2
(a) The HCF of 2xy z and –4x y is:
2
2
(i) 2x y (ii) –2x yz (iii) 2xy (iv) –2xyz
2
(b) The factors of 2x + x – 15 are:
(i) (x + 3)(2x – 5) (ii) (x – 3)(2x – 5) (iii) (x – 3)(2x + 5) (iv) (x + 3)(2x + 5)
3
3
3
(c) The HCF of 3x , 6y and 9z is:
(i) 1 (ii) 3 (iii) xyz (iv) 3xyz
2 3
4
3 2
(d) The HCF of 18x y , 36xy and –24x y is:
2 2
2
2 2
(i) –12x y (ii) –6xy (iii) 12x y (iv) 6xy 2
(e) The factors of (y – x)a + (x – y)b are:
(i) (x – y)(b – a) (ii) (y – x)(b – a) (iii) (x – y)(a – b) (iv) (y – x)(a + b)
2. Write True or False.
(a) An algebraic expression is a factor of another algebraic expression if the first can divide the second,
leaving behind a remainder.
(b) 1, 9, x, y, xy and 9xy are all the possible factors of 9xy.
2
(c) On factorizing x + 6x – 27, we get (x – 9)(x + 3).
(d) Grouping of terms for the factorization of an algebraic expression is done such that each group has
a common factor.
3. Fill in the blanks.

(a) Factors of a monomial consist of _________, their _________ and the _________ that can divide
the monomial exactly.
5 4
3 3
4 2
(b) The HCF of 5x y , 20x y and 25x y is _________.
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