Page 133 - Start Up Mathematics_8 (Non CCE)

(b) 12 – 4x – x 2
Taking –1 common from all the terms, we have
2
2
2
2
–1(x + 4x – 12) = –1{(x) + 2(x)(2) + (2) – (2) – 12}
2
= –1{(x + 2) – 4 – 12}
2
2
2
= –{(x + 2) – 16} = –{(x + 2) – (4) }
= –{(x + 2 + 4) + (x + 2 – 4)} Try It Out!
2
= –(x + 6)(x – 2) Factorize: 12x – 75y 2
EXERCISE 7.6
Factorize the following by completing the squares:

2
2
2
2
(a) x + 6x + 8 (b) 4x – 8x + 3 (c) x - 2 xy + y 2 - 1 (d) 1 x – 2x – 9
5 25 3
1 2 2 2 2
(e) a + a – 3 (f) x – 14x – 51 (g) a + 12a + 20 (h) x – 10x + 21
4
AT a Glance

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

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

4. When a common monomial factor occurs in each term of an algebraic expression then it can be expressed
as a product of HCF of its terms and the quotient of the given expression by the HCF of its terms.
5. 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.
6. If the given algebraic expression is the difference of two squares, then it can be factorized by using the
2
2
identity p – q = (p + q)(p – q).
7. 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
8. A quadratic polynomial can be factorized by using x + (a + b)x + ab = (x + a)(x + b).
Review Exercises
Multiple ChoiCe Questions
2
2
1. The HCF of 2xy z and –4x y is:
2
2
(a) 2x y (b) –2x yz (c) 2xy (d) –2xyz
2
2. The factors of 2x + x – 15 are:
(a) (x + 3)(2x – 5) (b) (x – 3)(2x – 5) (c) (x – 3)(2x + 5) (d) (x + 3)(2x + 5)
3
3
3
3. The HCF of 3x , 6y and 9z is:
(a) 1 (b) 3 (c) xyz (d) 3xyz
2 3
4
3 2
4. The HCF of 18x y , 36xy and –24x y is:
2
2 2
2 2
(a) –12x y (b) –6xy (c) 12x y (d) 6xy 2
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