Questions on Polynomials class 9 SET -1

Extra Questions on Polynomials Class 9

Q1. Find the remainder when \({y^3} + {y^2} - 2y + 5\) is divided by y - 5.

Q2. Determine the remainder when p(x) = \({x^3} + 3{x^2} - 6x + 15\) is divided by x - 2.

Q3.  When \(f(x) = {x^4} - 2{x^3} + 3b{x^2} - ax\) is divided by x+1 and x - 1, we get  remainder as 19 and 5 respectively. Find the remainder if f(x) is divided by x - 3.

Q4.  What must be subtracted from \(4{x^4} - 2{x^3} - 6{x^2} + x - 5\) so that the result is exactly divisible by \(2{x^2} + 3x - 2\) ?

Q5.  If (x + 1) and (x - 1) both are factors of \(a{x^3} + {x^2} - 2x + b\), find a and b.

Q6.  Factorize each of the following expressions:

1. \(48{x^3} - 36{x^2}\)
2. \(5{x^2} - 15xy\)
3. \(15{x^3}{y^2}z - 25x{y^2}{z^2}\)

Q7. Factorize:

1. \(2{x^2}(x + y) - 3(x + y)\)
2. \(5xy(5x + y) - 5y(5x + y)\)
3. \(x({x^2} + {y^2} - {z^2}) + y({x^2} + {y^2} - {z^2}) + z({x^2} + {y^2} - {z^2})\)
4. \(ab({a^2} + {b^2} - {c^2}) + bc({a^2} + {b^2} - {c^2}) + ca({a^2} + {b^2} - {c^2})\)

Q8. Factorize each of the following expressions:

1. \(25{x^2}{y^2} - 20x{y^2}z + 4{y^2}{z^2}\)
2. \(4{x^2} - 4\sqrt 7 x + 7\)
3. \(\dfrac{{{a^2}}}{{{b^2}}} + 2 + \dfrac{{{b^2}}}{{{a^2}}}\)
4. \(4{a^2} + 12ab + 9{b^2} - 8a - 12b\)

Q9. Factorize each of the following:

1. \(25{x^2} - 36{y^2}\)
2. \(2ab - {a^2} - {b^2} + 1\)
3. \(36{a^2} - 12a + 1 - 25{b^2}\)
4. \({a^4} - 81{b^4}\)
5. \({a^{12}}{b^4} - {a^4}{b^{12}}\)
6. \(4{x^2} - 9{y^2} - 2x - 3y\)

Q10. Factorize by completing the square.

1. \({a^4} + {a^2} + 1\)
2. \({y^4} + 5{y^2} + 9\)
3. \({x^4} + 4\)
4. \({x^4} + 4{x^2} + 3\)

Q11. Factorize by completing the square.

1. \({a^3} - 27\)
2. \(1 - 27{x^3}\)
3. \(8{x^3} - {(2x - 3y)^3}\)
4. \({a^8} - {a^2}{b^6}\)
5. \({a^3} - 5\sqrt 5 {b^3}\)

Q12. Factorize the following:

1. \(16{p^3}{q^2} + 54{r^3}\)
2. \(\dfrac{{{a^3}}}{8} + 8{b^3}\)
3. \(2\sqrt 2 {a^3} + 3\sqrt 3 {b^3}\)
4. \(8{a^4}b + \dfrac{1}{{125}}a{b^4}\)
5. \({a^7} - 64a\)

Q13.Q13. Factorize:

1. \({x^3} + 9{x^2} + 27x + 27\)
2. \({x^3} - 9{x^2}y + 27x{y^2} - 27{y^3}\)

Q14. Using identities, find the value of

1. 101²
2. 98²
3. (0.98)²
4. 101 × 99
5. 190 × 190 - 10 × 10

Q15. Expand using suitable identity

1. (x + 5y + 6z)²
2. (2a - 3b + 4c)²
3. ( - a + 6b + 5c)²
4. (- p + 4q - 3r)²

Q16. Expand using suitable identity

1. (2x + 5y)³
2. (5p - 3q)³
3. (- a + 2b)³

Q17. Evaluate using identities

1. 102³
2. 99³

Q18. Simplify : 

1. (2a + b)³ + (2a - b)³
2. (4x + 5y)³ - (4x - 5y)³

Q19. Factorize:

1. 30x³y + 24x²y² - 6xy
2. 5x(a - b) + 6y(a - b)

Q20. Factorize:

1. 9x² - y²
2. (3 - x)² - 36x²
3. (2x - 3y)² - (3x + 4y)²
4. 16x⁴ - y⁴

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