Page 383 - Start Up Mathematics_8 (Non CCE)

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(d) x + x + 1 (e) 3y + 5y – 7 (f) y + y + 1 Exemplar Problems
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(g) y – 3y + 4 (h) x – 1 1. c 2. x + 1 2 3. False
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2. (a) Quotient = 5x – 2x + 5 x ; Remainder = 6 4. 3(x + 4) 5. x – x + x
3 Chapter 7
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(b) Quotient = p – p – 1; Remainder = 1
(c) 2y – 5 Exercise 7.1
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4 3
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(d) Quotient = 4a + 3a – 2; Remainder = a – 1 1. (a) 3y (b) 4xy (c) 7x y
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5 6 4 3
3. 0 4. 7 (d) –2xy z (e) 9x y z u
Exercise 6.5 2. (a) 2xy(3x + 1) (b) 2(x – 6)(x – 2)
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(a) (7x – a – b) (b) (a + b ) (a – b) (a + b) (c) 2x y(–2 + 4xy + xy ) (d) x(y + 3z + x)
2 3 2
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(c) (2x + 3y + a + b) (d) 3(1 + 2x – 2y) (e) 16x y z (2xy – 3z ) (f) xy(ax + by + cz)
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2 2
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2
2 2
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2 2
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(e) 1 (f) a – b – a b (g) 18x z (2y z – 3x + 5x y ) (h) 12x y(4y z – 3x)
(i) (x + 4)(2x – 3) (j) 3x(6x – 5y)(3 – 4x)
Review Exercises
Multiple Choice Questions (k) (x – 2y)(2x – 4y – 3) (l) (x – y)(l – 3m + n(x – y))
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1. b 2. a 3. c 4. d 5. a (m) x (3x –y)(x + 1) (n) 2(x + y)(x – 4y)
Solve Mentally Exercise 7.2
Fill in the Blanks (a) (a – c)(b + d) (b) (y + 2z)(6x – y)
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1. constant term 2. bivariate 3. 2, 4 (c) (b – a)(b + a ) (d) (a – x)(a – 2y)
4. infinite 5. cubic 6. degree (e) (3y + x )(x – 2y) (f) (ya – x)(xa – y)
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Answer in One Word or a Line 2 2 2 2 2
1. The exponents of a polynomial can only be non-negative (g) 4(p – q) (2p – 2q – 3) (h) (l + m )(x + y )
integers. A polynomial cannot have infinite number of (i) (1 – x)(1 – y) or (x – 1) (y – 1)
terms.
2. In a bivariate polynomial, the sum of the exponents of Exercise 7.3
the variables in each term is calculated and the highest 1. (a) 3(4x + 9y)(4x – 9y) (b) (13x – 8y)(20y – x)
sum is called the degree of the polynomial. 1 1 ˆ Ê 1 1 ˆ
Ê
3. Every polynomial is an algebraic expression but not vice (c) Ê Á Ë x + ˜ Á x - ˜ (d) 62 + 1 ˆ Ê 2 - 1 ˆ ˜
˜ Á l
Á l
Ë
m
m
3
2
versa. For example, 5xy – 9x + 12y – 4 is a polynomial 4 13¯ Ë 4 13¯ 5 ¯ Ë 5 ¯
2
2
2
and an algebraic expression, but 9x y is only an algebraic (e) (a + 9b )(a + 3b)(a – 3b)
expression and not a polynomial. 4 4 2 2
4. If on dividing a polynomial by a binomial, the remainder (f) (16a + b )(4a + b )(2a + b)(2a – b)
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2
is zero then the binomial is a factor of the polynomial. (g) 8xy(x + y ) (h) 7(3xy + 1)(3xy – 1)
5. Polynomials of degree 1 are called linear polynomials, (i) (2 + l – m)(2 – l + m)
degree 2 are called quadratic polynomials, degree 3 1 3 ˆ Ê 1 3 ˆ
are called cubic polynomials and degree 4 are called (j) b 2 Ê Á a + c ˜ Á a – c ˜
biquadratic polynomials. Ë 6 7 ¯ Ë 6 7 ¯
Let’s Evaluate (k) (8p + 5q – 4)(8p – 5q – 4)
1. (a) 3 (b) 7 (c) 3 2. (a) 240 (b) 76 (c) 12,000 (d) 400
2 2
2
3 6 5 3
4 5
2. (a) 9x y (b) –9x y z (c) 56a b (d) 24p q r s Exercise 7.4
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2 3
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3. (a) 2x + 3x + 4x – 5x 2 (b) 3x y – 4xy + 5x y (a) (x + 1)(x + 1) (b) (3x – 4y)(3x – 4y)
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2
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4. (a) 3x + 3x + 2 (b) a + 5 (c) x + 6 (c) (x + 2)(x – 6) (d) l + 1ˆ Ê l + 1ˆ
˜ Á
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(d) Quotient = 2x – 2x – 1; Remainder = –6 Á Ë 2¯ Ë 2¯ ˜
5. 4x – 4 (e) (3c + a – 2b)(3c – a + 2b) (f) –(2x – y)(3x – y)
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6. (a) (3p – 4) (b) 4x
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2
2
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(g) (a + b )(a + b)(a – b) (h) (x + 2)(x + 2)
Thinking Skills (i) (x – 1)(x – 1) (j) (12 + x)(2 – x)
1. Yes 2. 2x + 5 3. y – 2
4. a = 2, b = –1 5. 3x – 1 (k) 3(3x – 2)(x – 2) (l) (2x + 3y)(2x + 3y – 4)
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