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Math Assignment Class IX Ch-2 | Polynomials
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Maths Assignment Class 9th
Chapter 2 Polynomials
Mathematics Assignment on Polynomials
Class IX Chapter 2
1. Find the value of p(x) = 3x2 - 2x + 8 at
2. Find the remainder when x3 - 3x2 + 3x - 1 is divided by
a) x - 1 Ans 0
b) x + 1 Ans -8
f) 3-x Ans 8
Q 3. a) Show that 2x - 3 is a factor of P(x) = 2x3 - 9x2 + x + 12.
b) Show that x + 2 is a factor of P(x) = x4 - x2 - 12.
Ans: P(-2) = 0 ⇒ x + 2 is the factor of P(x)
Hint: If remainder = 0 then given function is the factor of the given polynomial otherwise not.
a) 3x – kx + √3 Ans -3 - √3
b) √2x – kx + k + 2 Ans
d) x - 3x + kx Ans - 4
Q 7. If x - 5 is a factor of x3 + ax2 + bx - 20 and leaves a remainder -2 when divided by x - 3. Find a and b.
Ans (-9, 24)
Q 8. Factorize:
a) x2 + 11x + 30 : Ans (x + 5)(x + 6)
b) a2 - 16a + 63 :
Ans (a - 7)(a - 9)
c)15 - 2x - x2 :
Ans (3 - x)(5 + x)
d) 3 + 5x - 2x2 : Ans (1+ 2x)(3 - x)
e) 3m2 - 20m - 7 : Ans (3m+1)(m - 7)
f) 24m2 + m - 23 : Ans
(m + 1)(24m - 23)
g) 2x2 + 11xy - 21y :
Ans (x + 7y)(2x - 3y)
h) 7(x + y)2 + 48(x + y) - 7 : Ans (x + y + 7)(7x + 7y - 1)
I) 2m4n - 6m2n
+ 4n : Ans 2n(m+1)(m-1)(m2-2)
j) 36(a+3b)2 - 36(2a-3b)2 : Ans (16a+3b)(33b-4a)
k) x3 + 3x2 - 4x - 12 : Ans (x - 2)(x + 2)(x + 3)
l) 2x3 - 9x2 +x + 12 : Ans (x + 1)(x - 4)(2x - 3)
m) x3 -3x2 -10x+24 : Ans (x + 3)(x - 4)(3x - 2)
n) 2x3 -7x2 - 3x + 18 : Ans (x - 2)(x - 3)(2x + 3)
o) 3x3 + x2 - 38x + 24 : Ans (x - 3)(x + 4)(3x - 2)
p)(x3 - (y - z)3) : Ans
9. Evaluate by using identity:
a) 92×108 Ans:- 9936
b) 6.7×5.3 Ans:- 35.51
c)104×107 Ans:- 11128
10.Factorize:
a) 8x3 - 125y3 - z3 - 30xyz
b) 125x3 - 8 + 27y3 + 90xy
c) 3√3a3
- 5√5b3 - 8c3 - 6√15abc
d) (5a - 4b)3
+ (4b - 6c)3 + (6c - 5a)3
e) a3 + (a - 1)3 + (1 - 2a)3
f) (3x + 3y - 5z)3 + (2y + 3z - 5x)3 + (2z + 2x - 5y)3
g) (2x + y)3 - (x + y)3
h)
64m6-n6 : Ans:
(2mn + n)(4m - 2mn + n)(2m - n)(4m + 2mn + n)
11.Evaluate by using identity:
a) (-15)3 + (-13)3 + (28)3 Ans: 16380
b) (75)3 +
(-50)3 + (-25)3 Ans:
281250
Q 14.) If a3 + b3 + c3 = 3abc and a + b + c = 0 then show that
Q15.) If
26. If x3 + ax2+ bx + 6 has (x - 2) as a factor and leaves remainder 3, when divided by (x – 3), find a and b Ans[a = -3, b = -1]
27. For what value of a is 2x3 + ax2 + 11x + a + 3 divided by 2x - 1 Ans[a = -7 ]
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Comments
Very very nice assigament, thank ku so much.
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