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. \(2\sqrt 2 {x^2} + 9x + 5\sqrt 2 \)
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. \(2\sqrt 2 {x^3} + 3\sqrt 3 {y^3}\)
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. \({\left( {\dfrac{a}{b}} \right)^3} + {\left( {\dfrac{b}{c}} \right)^3} + {\left( {\dfrac{c}{a}} \right)^3} - 3\)
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: \({x^2} + \dfrac{1}{{{x^2}}} - 2\).

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. \({a^2} + \dfrac{1}{{{a^2}}} + 2\)
2. 3(x + 2)² + 17(x + 2) + 10
3. 4x² - 9y² + 20x + 25

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