3. 4. 5. 6.
7. 8. 9.
10. 11. 12. 13.
,
– x3 – 2x2 + x + 1 is divided by x - 1 .
Std 9 Holiday Assignment ( Maths A )
1. Write the coefficient of x2 in the following a) 2 + x2 + x b) 2 – 4x2 + x
2. Verify whether the following are the zeroes of the polynomial a P(x) = 3x -1 x = 1
3 211
b) P(x) = 3x -1 x =
√3
, -
√3
Find the remainder when x4
Using Factor Theorem determine whether g(x) is a factor of p(x)
i) P(x)= x3– 4x2+x+6 g(x)=x–3
ii) P(x) = 2x3 – 11x2 – 4x + 1 g(x) = 2x +1
Find the remainder when x3 – ax2 + 6x - a is divided by x - a .
Use suitable identities to find the products
i) ( x – 4 ) (x + 10) ii) ( 3x + 4 ) ( 3x – 5 ) iii) ( -3a +5b + 4c)2 Evaluate without actual multiplication
i) 95 x 96 ii) 103 x 107
Factorise using suitable identities
One of the factors of x4 +x2 – 20 is x2 + 5 , find the other factors. What must be added to 2x2 – 5x + 6 to get x3 - 3x2 + 3x -5 ?
If x + 2k is a factor of f(x) = x5 -4k2x3 + 2x +2k +3 , find ‘k’. By actual division find the quotient and remainder
i) 9x2 + 6xy + y2 Factorise
i) 6x2 + 5x – 6
ii) X2 –X+110
iii) 25y2 + 110y + 121 vi ) 25x2 + 36y2 + 49z2 + 60xy – 84yz – 70zx
iv)
i) ii) iii)
3x4 – 4x3 – 1 is divided by x + 1
p(x) = x5 + x4 + x3 +x2 + 2x + 2 by g (x) = x3 + 1
ii) 4y2 – 4y +1 iii) 8 + 64x3
iv) x3 + 13x2 + 32x + 20 vii)
v) 6x2 –17x+12 viii)4y3–2y2 –4y+2
p(x) = x6 + 3x2 +10 by q(x) = x4 +1
Using factor theorem factorise the polynomial x3 – 2x2 – x + 2
14.
15.If ( x3 + ax2 + bx + 6 ) has ( x – 2 ) as a factor and leaves a remainder 3
when divided by (x – 3 ) , find the values of ‘a’ and ‘b’ .
iv) ( 0.1x – 0.2y)2 x3 - 3x2 - 9x – 5