Question 1.
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
Solution:
Question 4.
Find the zero of the polynomial in each of the following cases
- (i) p(x)=x+5
- (ii) p (x) = x – 5
- (iii) p (x) = 2x + 5
- (iv) p (x) = 3x – 2
- (v) p (x) = 3x
- (vi) p (x)= ax, a≠0
- (vii) p (x) = cx + d, c≠0 where c and d are real numbers.
Solution:
(i) We have, p (x)= x+ 5
Now, p (x) = 0
⇒ x+ 5 = 0
⇒ x = -5
∴ – 5 is a zero of the polynomial p (x).
(ii) We have, p (x) = x – 5
Now, p (x) = 0
⇒ x – 5 = 0
⇒ x = 5
∴ 5 is a zero of the polynomial p (x).
(iii) We have, p (x) = 2x + 5
Now, P (x)= 0
⇒ 2x+ 5= 0
⇒ x = –5/2
∴ –5/2 is a zero of the polynomial p (x).
(iv) We have, p (x)= 3x- 2
Now p(x) = 0
⇒ 3x- 2 = 0
⇒ x= 2/3
∴ 2/3 is a zero of the polynomial p (x).
(v) We have, p (x) = 3x
Now, p (x)= 0
⇒ 3x=0
⇒ x =0
∴ 0 is a zero of the polynomial p (x).
(vi) We have, p (x)= ax, a≠0
Now, p (x)= 0 ⇒ ax= 0
⇒ x= 0
∴ 0 is.a zero of the polynomial p (x).
(vii) We have, p (x) = cx + d,c≠0
Now, p (x) = 0
⇒ cx + d = 0
x = - d/c
∴ - d/c is a zero of the polynomial p (x).
Question 1.
Determine which of the following polynomials has (x +1) a factor.
Question 2.
Use the Factor Theorem to determine whether g (x) is a factor of p (x) in each of the following cases
Question 1.
Use suitable identities to find the following products
(i) (x + 4)(x + 10)
(ii) (x+8) (x -10)
(iii) (3x + 4) (3x - 5)
Question 2.
Evaluate the following products without multiplying directly
- (i) 103 x 107
- (ii) 95 x 96
- (iii) 104 x 96
Solution:
Question 3.
Factorise the following using appropriate identities
Question 4.
Expand each of the following, using suitable identity
Question 6.
Write the following cubes in expanded form
Solution:
Question 9.
Verify
Question 14.
Without actually calculating the cubes, find the value of each of the following
Question 15.
Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given
Question 16.
What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
