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Question on Polynomials Class 9 SET - 2

Questions on Polynomials Class 9 SET - 2

Q1. Factorize the following by splitting the middle term:

    1. 3x2 + 19x + 30
    2. 22x2+9x+52
    3. 3x2 - 13x + 10

Q2. Factorize the following by factor theorem:

    1. x3 + 9x2 + 23x + 15
    2. x3 + 6x2 + 11x + 6

Q3. Factorize the following by using a suitable identity:

    1. 4x2 + 12xy + 9y2
    2. 2a5 - 54a2
    3. 22x3+33y3
    4. x5 - x
    5. x6 - y6
    6. (a - b)3 + (b - c)3 + (c - a)3
    7. x8 - y8
    8. 27x3 - 135x2 + 225x - 125

Q4. Evaluate the following by using a suitable identity:

    1. 9983
    2. (10.2)3
    3. 9982 - 4
    4. 9992 - 1
    5. (-25)3 + 103 + 153
    6. 10.2 × 9.8
Q5. If 5 is a zero of x3 + 5x2 + 2x + 8, find k.

Q6. If (x - 2) is a zero of x3 - 4x2 + kx - 8, find k.

Q7. If (x - 2) and (x + 3) are factors of x3 + ax2 + bx - 30, find a and b.

Q8. If x + y + z = 8 and xy + yz + zx = 20, find the value of x3 + y3 + z3 - 3xyz.

Q9. If a + b + c = 9 and a2 + b2 + c2 = 35, find the value of a3 + b3 + c3 - 3abc.

Q10. Find the value of (2.7)3 - (1.6)3 - (1.1)3 using a suitable identity.

Q11. Factorize the following by using a suitable identity:

    1. a3 + b3 - 8c3 +6abc
    2. (ab)3+(bc)3+(ca)33
    3. 8x3 - 27y3 + 125z3 + 90xyz

Q12. Find the value of a3 + 8b3, if a + 2b = 10 and ab = 15.

Q13. Find the value of a3 + 27b3, if a - 3b = - 6 and ab = - 10.

Q14. find the value of m and n, if y2 -1 is a factor of y4 + my3 + 2y2 - 3y + n.

Q15. (x + 2) is a factor of mx3 + nx2 + x - 6. it leaves the remainder 4 when divided by (x - 2). find m and n. 

Q16. The polynomials kx3 + 3x2 - 3 and 2x3 - 5x + k leave the same remainder when divided by (x - 4). Find k.

Q17. Factorize: x2+1x22.

QQ18. If ab + bc + ca = 10 and a2 + b2 + c2 = 44. find a3 + b3 + c3 - 3abc.

Q19. Show that x - 2 is a factor p(x) = x3 - 12x2 + 44x - 48.

Q20. Factorize: x3 - 2x2 - 5x + 6.

Q21. If x + p is a factor of p(x) = x5 - p2x3 + 44x - 40. Find p.

Q22. Factorize:

    1. a2+1a2+2
    2. 3(x + 2)2 + 17(x + 2) + 10
    3. 4x2 - 9y2 + 20x + 25
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