GSEB Solutions for Class 6 Mathematics – Polynomial

GSEB Solutions for Class 6 Mathematics – Polynomial

GSEB SolutionsMathsScience
Activity

Solution 1:

1. 4x², 7x² and 2x²
2. -y³, -y³ and 3y³
3. 2xy² and 3xy²
4. 6x⁷ and x⁷

Solution 2:

1. 5x, 2x²
2. -3x, 7x²
3. 8xy³, 8yx³
4. a²b², 7ab
5. -x, 5x

Solution 3:

4x², -y²
4b², p²
4x², p²
(Note: Many more answers are possible.)

Exercise 

Solution 1:

Solution 2:

The polynomials having constant terms are given below.
4x² + 2x – 3, x + 4, 6a² + 5ab + 7, 16, 6x² – 6x + 5

Solution 3:

(1) The pairs of like terms are: 4x²and 3x²;– x and – 2x.
(2) The pairs of like terms are: – 8x² and 7x²;7x and – 2x; 3y and -y.
(3) The pairs of like terms are: 2ab and – ab; b² and 3b² .
Solution 4:

(1) m + 3 = 2 + 3 = 5
(2) 4m² = 4 × (2 × 2) = 4 × 4 = 16
(3) m² + 6 = (2 × 2) + 6 = 4 + 6 = 10
(4) 3n² = 3(1 × 1) = 3
(5) 5m – 6n = (5 × 2) – (6 × 1) = 10 – 6 = 4
(6) mn – n = (2 × 1) – 1 = 2 – 1 = 1
(7) n² + 3mn = (1 × 1) + 3(2 × 1) = 1 + 6 = 7
(8) 2m – 3n² = (2 × 2) – 3(1 × 1) = 4 – 3 = 1
(9) 3m² – 12mn + 4n²
= 3(2 × 2) – 12(2 × 1) + 4(1 × 1)
= 3(4) – 12(2) + 4
= 12 – 24 + 4
= 16 – 24
= (-8)
(10) 3n – 2m² + 3
= 3(1) -2(2 × 2) + 3
= 3 – 2(4) + 3
= 3 – 8 + 3
= 6 – 2
= (-2)

Practice – 1

Solution 1:

(1) 7x³ + 8x² + 9xy + 4y²
There are 4 terms in the polynomial.
(2) 2xy + 3x² – 25y³
There are three terms in the polynomial.
(3) a²bc
There is only on term in the polynomial.
(4) 6a + 5b – 10ab – a² – b²
There are five terms in the polynomial.

Solution 2:

Polynomials having different terms:
1) 6a + 5b – 10ab
2) 10ab – a²bc
3) 2a²b²
4) 8ab⁴c
5) 6a -3b
6) y² + 2xy + 3x²

Solution 3:

The polynomials written in question 2 can be classified into monomials, binomials and trinomials as follows:

Practice – 2

Solution 1:

The monomials from the list of given polynomials are as follows:
8ab, -9x², -7x²y², 9abc

Solution 2:

The table below shows three illustrations each of monomial, binomial and trinomial:

Practice – 3

Solution 1:

Solution 2:

Solution 3:

(1) The coefficient of the term x² is 1.
[x² = 1 × x²]
(2) The power of the term 3abc is 3.
The power of the term 3abc is = 1 + 1 + 1 = 3
(3) The power of the term 7 in 12x + 7 is 0.
7 is the constant term and in a constant term, the power of the variable is zero.
7 = 7 × x⁰ …. (x⁰ = 1)

Practice – 4

Solution 1:

The pairs of like terms are:

1. 7x² and -5x²
2. -3y² and -10y²
3. 3a²b² and 6a²b²
4. xy and 3xy

Solution 2:

The pairs of unlike terms are:
(1) 5x and 3xy
(2) -3y² and -5x²
(3) xy and 7ab
(4) -10y² and 6a²b²
[Note: Many more pairs of unlike terms are possible in the given example.]

Practice – 5

Solution 1:

(1) x + y = 1 + 3 = 4
(2) x + y – a = 1 + 3 + 2 = 6
(3) 4x – y = 4 + 3 = 1
(4) a² – x = (2 × 2) – 1 = 4 – 1 = 3
(5) x² = (x × x) = (1 × 1) = 1
(6) 3a + xy = (3 × 2) + (1 × 3) = 6 + 3 = 9
(7) y² – a² = (y × y) – (a × a) = (3 × 3) – (2 × 2) = 9 – 4 = 5
(8) x² – 6xy + y² = (x × x) – 6 × x × y + (y × y)
= (1 × 1) – (6× 1 × 3) + (3 × 3)
= 1 – 18 + 9
= -8
(9) 4x² + 2xy + 9y² = 4(x × x) + 2 × x × y + 9(y × y)
= 4(1 × 1) + (2 × 1 × 3) + 9(3 × 3)
= 4 + 6 + 81
= 91
(10) a² – 6ax + 9x²
= (a × a) – (6 × a × x) + 9(x × x)
= (2 × 2) – (6 × 2 × 1) + 9(1 × 1)
= 4 – 12 + 9
= 13 – 12 = 1