Page 121 - Start Up Mathematics_8 (Non CCE)

2
2
4
+
-
p - q 4 ( p + q ) ( pq) ( pq) 2 2
\ = = (p + q ) (p + q)
-
( pq- ) ( pq) (Cancelling the common factor)
2
2
(b) (x + y) – (a – b) ÷ (x + y – a + b)
2
2
2
2
(x + y) – (a – b) = (x + y + a – b) {x + y – (a – b)} {Using p – q = (p + q)
= (x + y + a – b) (x + y – a + b) (p – q)}
-
2
y ab
(x + ) y - (ab ) 2 (x ++ - ) (x + -+ )
y ab
\ = = x + y + a – b
y ab
y ab
(x +- + ) (x +- + )
EXERCISE 6.5
Divide using the factorization method:
8
2
2
8
2
2
(a) 49x – (a + b) by (7x + a + b) (b) (a – b ) by (a + b )
2
2
2
(c) (2x + 3y) – (a + b) by (2x + 3y – a – b) (d) (3 – 12 (x – y) ) by (1 – 2x + 2y)
4 4
2 2
4 2
2 4
2
2
(e) (x – 1) – (x – 2) by (2x – 3) (f) (a b – a b – a b ) by a b
AT a Glance
1. For a polynomial in one variable, the highest power of the variable is called its degree.
2. A polynomial consisting of only a constant is called a constant polynomial. The degree of a constant
polynomial is zero.
3. A polynomial of degree 1 is called a linear polynomial, degree 2 is called a quadratic polynomial,
degree 3 is called a cubic polynomial and degree 4 is called a biquadratic polynomial.
4. Division Algorithm: Dividend = Divisor × Quotient + Remainder
Review Exercises
Multiple ChoiCe Questions
2
5
1. The degree of the polynomial 7x + 3x + 4x + 1 is:
(a) 6 (b) 5 (c) 4 (d) 2
6 2
3 3
2. The degree of the polynomial x y + 7x y + 9 is:
(a) 8 (b) 6 (c) 9 (d) 12
3 4
2
4 3
3. (32x y – 16x y ) ÷ (–8x y) is equal to:
2 2
3
2 2
2 2
2 2
(a) –6x y (b) –8x y (c) –4x y + 2xy (d) –2x y
2
4. 4a + 4a +1 divided by (2a + 1) gives quotient as:
(a) 2a – 1 (b) a + 1 (c) a – 1 (d) 2a + 1
2
2
5. If x – 3y exactly divides x – 7xy + 12y , the remainder is:
(a) 0 (b) 1 (c) –1 (d) cannot say
solve Mentally
Fill in the Blanks
1. A polynomial consisting of only a ______________ is called a constant polynomial.
2. Polynomials with two variables are called ______________ polynomials.
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