BUDS PUBLIC SCHOOL
WORKSHEET 2*
MATHEMATICS
GRADE 9
Polynomials
b) √6 c) 16
1. Find the degree of polynomial of the following polynomials: a) 6 – x2 + 8x
d) 3x
f) 7x6 + 2x3 – 1
e) 9 – y
g) 2y8 – 5y 10 + 10y6
b) xy in 5xyz2
2. Write the co-efficient of: a) y in -3xy
i) 3x + x3 – 5x2
h) -2 + m
c) a2 in a3 - 5a2 +7
3. From the given expressions separate monomials, binomials, trinomials
3/2 x, -6 + 3x, 4 – 2y +y3 , 8 + 2x , 3 x 2x -10 +y , 4+ 2z/5 ,
7x2 – 8x +3,
2a – 3b,
4a +2x – 3y,
2 + 5y – y2
4. Which of the algebraic expression is a polynomial: i) 2 + 4x – 7x2
ii) 3y – 1/y
iv) 5√z + z2
iii) 5√x + 8x + 2
5. Find the value of the polynomial 3x2 – 2x + 8 at i) x = 0
ii) x = 2
iii) x = -2
6. Find the zero of the polynomial in each of the following cases: i) f(x) = x – 3
iii) f(z) = z +7
iv) p(x) = 4x – 5
ii) f(y) = 2y + 5
v) p(y) = 2y – 1
7. Find the remainder when polynomial f(x) = 3x2 – 2x + 1 is divided by :
i) x – 2
ii) x + 1
iii) x
iv) x + 3
v) x + 4
vi) 2x + 1
vii) 3x – 2
viii) x – 3
8. Determine (x – 1) is a factor of which of the following polynomials:
i) x3 – 3x2 + 3x – 1
9. Factorise:
ii) 4x2 – 3x + 2
i) x2 – 4
ii) 9 – x2
iii) 3x3 + 4x2 – 7x + 2
iii) 9m2 – 25n2
10. Expand: i) (3x + 2y)2 ii) (2a + 5b)2
vii) (x + 7) (x + 12)
viii) (y - 8) (y + 35)
xi) (2x + 3y + 4z)2
xii) (5a – 3b + 2c)2
iv) a2b2 – 121
iii) (4x + 3)2 iv) (10x + 3)2
ix) (8x + 3y)(5x + 2y)
xiii) (x + 3)3
v) x2 + x – 6
v) (2x - 5y)2 vi) (5x - 8y)2
x) (4a + 5) (2a + 9)
xiv) (2a – 5)3
WORKSHEET 2**
1. Verify whether the indicated numbers are zeros of the polynomial corresponding to them in
the following cases:
i) f(x) = 2x2 – x- 3 ; x = - 1
ii) p(m) = m(m-4); m = 2
iv) q(x) = x2 – 9 ; x = -3, 3
v) p(x) = x3 – 4x2 ; x = 0, 4
iii) f(y) = 2y2 – y – 1; y= - ½
vi) r(x) = 3s2 – 8; s = 3
2. Use the remainder theorem to find the remainder when x3 – 3x2 + 3x – 1 is divided by:
i) x - 1
ii) x + 1
iii) x – ½
iv) 2x + 1
3. Using factor theorem to determine whether g(x) is a factor of p(x) in each of the following
cases: i) p(x) = x3 + 5x2 + 7x + 3 ; g(x) = x + 1
ii) p(x) = x3 - 2x2 – 5x - 3
4. Factorise : i) x2 + 11x +30
ii) a2 – 16a +63
iii) x2 + 2x -35
iv) 15 – 2x – x2
5. Factorise, using remainder theorem, each of the following polynomials:
i) x2 – 3x – 10
ii) y2 + 6y – 16
iii) 2z2 + 3z + 1
iv) 3x2 – 4x – 4
v) 6x2 + x - 1
6. Factorise i) a3 – b3 + c3 + 3abc ii) 8x3 – 125 y3 – z3 – 30 xyz
iii) 125x3 – 8 + 27y3 + 90xy
iv) 27x3 + y3
v) 8a3 +36a2b + 54 ab2 + 27b3
vi) 8x3 – y3 -12x2y + 6xy2
vii) a3 – 27b3 +2a2b – 6ab2
7. Expand i) (2x – 1/x)2 ii) (2x + y)(2x – y)
v) (-3x +y + z)2
vi) (m + 2n – 5p)2
iii) (a + 2b + c)2
iv) (2a – 3b – c)2
vii) (1/x + y/3)3
viii) (4 – 1/3x)3
8. If a+b = 10 and ab = 21, find the value of a3 + b3
9. Simplify i) (x + 3)3 + (x - 3)3
10. Simplify i) (a + b + c)2 + (a – b + c)2
ii) (2x + p – c)2 - (2x – p +c)2
11. If a + b+ c = 0 and a2 + b2 +c2 = 16, find the value of ab + bc + ca.
12. Find the value of 4x2 + y2 + 25z2 + 4xy – 10yz – 20zx when x = 4, y= 3, and z = 2
13. If a + b+ c = 0 then prove that a3 + b3+ c3 = 3abc
WORKSHEET 2***
1. If zero of the polynomial p(x) = x + a is x = -3, find ‘a’.
2. If zero of the polynomial f(y) = 2y - m is y = 2, find ‘m’.
3. If zero of the polynomial q(z) = az + 7 is x = -1, find ‘a’.
4. If zero of the polynomial p(y) = c – 3y is y = -2, find ‘c’.
5. Find out whether (x + 4) is a factor of x3 + x2-5x + 2 or not.
6. Use remainder theorem to show that (x + 1) is a factor of 9x3 + 15x2 – 6x - 12
7. Show that: i) (2x – 3) is a factor of 2x3 – 9x2 + x + 12
ii) (x+ 2) is a factor of x4 – x2 – 12
8. Find the value of k, if x + 1 is a factor of p(x) in each of the following cases:
i) p(x) = x3 – 3x2+ kx
ii) p(x) = 3x2 – kx + √3
iii) p(x) = kx3 – 9x2 + x + 6k
9. (x – 2) and (x + 3) are the factors of p(x) = ax3 + 3x2 –bx - 12. Find the values of a and b.
10. Factorise:
i) 3x2 – 4x +1
ii) 3x2 + x - 2
iii) 12a2 + 11a – 5
11. Factorise, using factor theorem: i) x3 + 3x2 – 4x - 12
iii) x3 – 3x2 -10x +24
iv) 2x3 – 7x2 -3x +18
ii) 2x3 – 9x2 + x + 12
v) 3x3 + 10x2 + x - 6
12. Evaluate, using appropriate identities: i) (103)2
v) (999)3
vi) 104 x 107
ii) (207)2
13. Expand: i) (1/3 a + ½ b – 1)2
iii)( 2x – 1/x – 3)2
ii) (x – 1/x + 1)2
iv) 24m2 + m – 23
iii) (97)2
i v) (103)3
iv) (5 – 3x – 1/3x)2
14. Give possible expressions for length and breadth of each of the following rectangles, whose
areas are: i) (x2 – 6x – 7) sq. unit
ii) (2x2 + 5x -3) sq. unit ( Hint: factorise the polynomial)
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