Which of the following expressions are polynomials?

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x) 1

(xi)

(xii)

In case of a polynomial, write its degree.

Write the degree of each of the following polynomials:

(i)

(ii)

(iii) 9

(iv)

(v)

(vi)

Write:

(i) Coefficient of in

(ii) Coefficient of

(iii) Coefficient of in

(iv) Coefficient of in

Give an example of a binomial of degree 27.

Give an example of a monomial of degree 16.

Give an example of a trinomial of degree 3.

Classify the following as linear, quadratic and cubic polynomials:

(i)

(ii)

(iii)

(iv) -7+z

(v) (vi)

Iffind

(i) p (0)

(ii)p(3)

(iii) p(-2)

If find

(i) P(0)

(ii) p(2)

(iii) p(-1)

If find

(i) f (0)

(ii) f (4)

(iii) f (-5)

Find the zero of the polynomial:

(i) P(x)=x-5

(ii) q(x)=x+4

(iii) p(t)=2t-3

(iv) f(x)=3x+1

(v) g(x)=5-4x

(vi) h(x)=6x-1

(vii) p(x)=ax + b,a≠0

(viii) q(x) = 4x

(ix) p(x)=ax,a≠0

Verify that:

(i) 4 is a zero of the polynomial p(x)=x-4.

(ii) -3 is a zero of the polynomial p(x) = x + 3.

(iii) -1/2 is a zero of the polynomial p(y)=2y+1.

(iv) 2/5 is a zero of the polynomial p(x) =2-5x.

(v) 1 and 3 are the zeros of the polynomial p(x)=(x-1)(x-2)

(vi) 0 and 3 are the zeros of the polynomial p(x) =x² - 3x

(vii) 2 and-3 are the zeros of the polynomial p(x) =x² + x - 6

is divided by (x-1)

is divided by (x-3)

is divided by (x-2)

is divided by (x-6)

is divided by (x+2)

is divided by (x+3)

is divided by (2x-1)

is divided by (3x+2)

is divided by (x-a)

The polynomials and when divided by (x-4) leave the same remainder. Find the value of a.

The Polynomial f(x) = x⁴ -2x³ +3x² -ax + b when divided by (x-1) and (x+1) leaves the remainders 5 and 19 respectively. Find the values of a and b. Hence, find the remainder when f(x)  is divided by (x-2).

(x-2) is a factor of

(x-3) is a factor of

(x-1) is a factor of

(x+2) is a factor of

(x+5) is a factor of

(2x-3) is a factor of

is a factor of

is a factor of

Find the value of k for which (x-1) is a factor of

Find the value of a for which (x-4) is a factor of

Find the value of a for which the polynomial is divisible by (x+3).

For what value of a is the polynomial exactly divisible by (2x-1)?

Find the values of a and b so that the polynomial is exactly divisible by (x-1) as well as (x-2).

Find the values of a and b so that the polynomial is

exactly divisible by (x+2) as well as (x+3).

Without actual division, show that is exactly divisible by .

If has (x-2) as a factor and leaves a remainder 3 when divided by (x-3), find the values of a and b.

Factorize:

9x² + 12xy

Factorize:

18x²y – 24 xyz

Factorize:

27a³b³ – 45a⁴b²

Factorize:

2a(x + y) -3b(x + y)

Factorize:

2x(p² + q²) +4y (p² + q²)

Factorize:

x(a - 5) + y (5 - a)

Factorize:

4(a + b) – 6 (a + b)²

Factorize:

8(3a – 2b)² – 10 (3a – 2b)

Factorize:

x(x + y)³ – 3x²y (x + y)

Factorize:

x³ + 2x² + 5x + 10

Factorize:

x² + xy – 2xz – 2yz

Factorize:

a³b – a²b + 5ab – 5b

Factorize:

8 – 4a – 2a³ + a⁴

Factorize:

x³ – 2x²y + 3xy² – 6y³

Factorize:

px – 5q + pq – 5x

Factorize:

x² + y – xy - x

Factorize:

(3a - 1)² – 6a + 2

Factorize:

(2x - 3)² – 8x + 12

Factorize:

a² + a – 3a² - 3

Factorize:

3ax – 6ay – 8by + 4bx

Factorize:

abx² + a²x + b²x + ab

Factorize:

x³ – x² + ax + x – a – 1

Factorize:

2x + 4y – 8xy – 1

Factorize:

ab(x² + y²) – xy(a² + b²)

Factorize:

a² + ab(b + 1) + b³

Factorize:

a³ + ab(1 – 2a) – 2b²

Factorize:

2a² + bc – 2ab – ac

Factorize:

(ax + by)² + (bx - ay)²

Factorize:

a(a + b – c) – bc

Factorize:

a(a – 2b – c) + 2bc

Factorize:

a²x² + (ax² + 1)x + a

Factorize:

ab(x² + 1) + x(a² + b²)

Factorize:

x² – (a + b)x + ab

Factorize:

Factorize:

25x² – 64y²

Factorize:

100 – 9x²

Factorize:

5x² – 7y²

Factorize:

(3x + 5y)² – 4z²

Factorize:

150 – 6x²

Factorize:

20x² – 45

Factorize:

3x³ - 48

Factorize:

2 – 50x²

Factorize:

27a² – 48b²

Factorize:

x – 64x³

Factorize:

8ab² – 18a³

Factorize:

3a³b – 243ab³

Factorize:

(a + b)³ – a – b

Factorize:

108a² –3(b – c)²

Factorize:

x³ – 5x² – x + 5

Factorize:

a² + 2ab + b² – 9c²

Factorize:

9 – a² + 2ab – b²

Factorize:

a² – b² –4ac + 4c²

Factorize:

9a² + 3a – 8b – 64b⁴

Factorize:

x² – y² + 6y – 9

Factorize:

4x² – 9y² – 2x – 3y

Factorize:

x⁴ – 1

Factorize:

a – b – a² + b²

Factorize:

x⁴ – 625

Factorize:

x² + 11x + 30

Factorize:

x² + 18x + 32

Factorize:

x² + 7x – 18

Factorize:

x² + 5x – 6

Factorize:

y² – 4y + 3

Factorize:

x² – 21x + 108

Factorize:

x² – 11x – 80

Factorize:

x² – x – 156

Factorize:

z² – 32z – 105

Factorize:

40 + 3x – x²

Factorize:

6x – x – x²

Factorize:

7x² + 49x + 84

Factorize:

m² + 17mn – 84

Factorize:

5x² + 16x + 3

Factorize:

6x² + 17x + 12

Factorize:

9x² + 18x + 8

Factorize:

14x² + 9x + 1

Factorize:

2x² + 3x – 90

Factorize:

2x² + 11x – 21

Factorize:

3x² – 14x + 8

Factorize:

18x² + 3x – 10

Factorize:

15x² + 2x – 8

Factorize:

6x² + 11x – 10

Factorize:

30x² + 7x – 15

Factorize:

24x² – 41x + 12

Factorize:

2x² – 7x – 15

Factorize:

6x² – 5x – 21

Factorize:

10x² – 9x – 7

Factorize:

5x² – 16x – 21

Factorize:

2x² – x – 21

Factorize:

15x² – x – 28

Factorize:

8a² – 27ab + 9b²

Factorize:

5x² + 33xy – 14y²

Factorize:

3x³ – x² – 10x

Factorize:

Factorize:

Factorize:

Factorize:

Factorize:

Factorize:

Factorize:

Factorize:

Factorize:

Factorize:

Factorize:

2(x + y)² –9(x + y) – 5

Factorize:

9(2a – b)² – 4(2a – b) – 13

Factorize:

7(x – 2y)² – 25(x – 2y) + 12

Factorize:

4x⁴ + 7x² – 2

Expand:

(i) (a + 2b + 5c)²

(ii) (2a – b + c)²

(iii) (a – 2b – 3c)²

Expand

(i) (2a – 5b – 7c)²

(ii) (–3a + 4b – 5c)²

(iii)

Factorize:

4x² + 9y² + 16z² + 12xy – 24yz – 16xz

Factorize:

9x² + 16y² + 4z² –24xy + 16yz – 12xz

Factorize:

25x² + 4y² + 9z² – 20xy – 12yz + 30xz

Evaluate:

(i) (99)²

(ii) (998)²

Expand:

(i) (3x + 2)²

(ii) (3a – 2b)²

(iii)

Expand:

(i)

(ii)

(iii)

Evaluate:

(i) (95)³

(ii) (999)³

Factorize:

x³ + 27

Factorize:

8x³ + 27y³

Factorize:

343 + 125 b³

Factorize:

1 + 64x³

Factorize:

Factorize:

Factorize:

16x⁴ + 54x

Factorize:

7a³ + 56b³

Factorize:

x⁵ + x²

Factorize:

a³ + 0.008

Factorize:

x⁶ + y⁶

Factorize:

2a³ + 16b³ – 5a – 10b

Factorize:

x³ + 512

Factorize:

64x³ – 343

Factorize:

1 – 27 x³

Factorize:

x³ – 125y³

Factorize:

Factorize:

a³ – 0.064

Factorize:

(a + b)³ – 8

Factorize:

x⁶ – 729

Factorize:

(a + b)³ – (a – b)³

Factorize:

x⁶ – 729

Factorize:

32x⁴ – 500x

Factorize:

3a⁷b – 81a⁴b⁴

Factorize:

Factorize:

8a³ – b³ – 4ax + 2bx

Factorize:

a³ + 3a²b + 3ab² + b³ – 8

Factorize:

125a³ + b³ + 64c³ – 60abc

Factorize:

a³ + 8b³ + 64c³ – 24abc

Factorize:

1 + b³ + 8c³ – 6bc

Factorize:

216 + 27b³ + 8c³ – 108bc

Factorize:

27a³ – b³ + 8c³ + 18abc

Factorize:

8a³ + 125b³ – 64c³ + 120abc

Factorize:

8 – 27b³ – 343c³ – 126bc

Factorize:

125 – 8x³ – 27y³ – 90xy

Factorize:

Factorize:

x³ + y³ – 12xy + 64

Factorize:

(a – b)³ + (b – c)³ + (c – a)³

Factorize:

(3a – 2b)³ + (2b – 5c)³ + (5c – 3a)³

Factorize:

a³(b – c)³ + b³(c – a)³ + c³(a – b)³

Factorize:

(5a – 7b)³ + (9c – 5a)³ + (7b – 9c)³

Find the product:

(x + y – z)(x² + y² + z² – xy + yz + zx)

Find the product:

(x –2y – 3)(x² + 4y² + 2xy – 3x + 6y + 9)

Find the product:

(x – 2y – z)(x² + 4y² + z² + 2xy + zx + 2yz)

If find the value of

If find the value of

Which of the following expressions is a polynomial in one variable?

Which of the following expressions is a polynomial?

Which of the following is a polynomial?

Which of the following is a polynomial?

Which of the following is a polynomial?

Which of the following is a quadratic polynomial?

Which of the following is a linear polynomial?

Which of the following is a binomial?

is a polynomial of degree

Degree of the zero polynomial is

Zero of the polynomial p(x) = 2x + 3 is

Zero of the polynomial p(x) = 2 - 5x is

Zero of the zero polynomial is

If p(x) = x + 4, then p(x) + (-x) =?

If then

The zeroes of the polynomial p (x) = x² + x - 6 are

The zeroes of the polynomial p (x) = 2x² + 5x - 3 are

If (x²+ kx – 3) = (x – 3 ) (x + 1) then k =?

If (x + 1) is a factor of 2x²+ kx, then k =?

The coefficient of the highest power of x in the polynomial 2x² – 4x⁴ + 5x² – x⁵ + 3 is:

When (x³¹ + 31) is divided by (x + 1), the remainder is

When p (x) = x³ – ax² + x is divided by (x – a), the remainder is

When p (x) = (x³ + ax² + 2x + a) is divided by (x + a), the remainder is

When p (x) = x⁴ + 2x³ – 3x² + x – 1 is divided by (x – 2), the remainder is

When p(x) = x³ - 3x² + 4x + 32 is divided by (x + 2), the remainder is

When p (x) = 4x³ - 12x² + 11x – 5 is divided by (2x – 1), the remainder is

(x +1) is a factor of the polynomial:

4x² + 4x – 3 = ?

6x² + 17x + 5

x² - 4x – 21 = ?

If (x + 5) is a factor of p (x) = x³ – 20x + 5k, then k =?

3x³ + 2x² + 3x + 2 = ?

If where and then the value of is

If a + b + c = 0, then a³ + b³ + c³ = ?

(x + 2) and (x – 1) are factors of (x³ + 10x² + mx + n) then

The value of (369)² – (368)² = ?

104 x 96 =?

4a² + b² + 4ab + 8a + 4b + 4 = ?

The coefficient of x in the expansion of (x + 3)³ is

If a + b + c = 0, then

If x + y + z = 9 and xy + yz + zx = 23, then the value of (x³ + y³ + z³ – 3xyz) = ?

If (x¹⁰⁰ + 2x⁹⁹ + k) is divisible by (x + 1), then the value of k is

In a polynomial in x, the indices of x must be

For what value of k is the polynomial p (x) = 2x³ – kx² + 3x + 10 exactly divisible by (x + 2)?

207 x 193 =?

305 x 308 =?

The zeroes of the polynomial p (x) = x² – 3x are

The zeroes of the polynomial p (x) = 3x² – 1 are

The question consists of two statements, namely, Assertion (A) and Reason (R), Please select the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R), Please select the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R), Please select the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R), Please select the correct answer.

Match the following columns:

The correct answer is:

(a)-……., (b)-……., (c)-……., (d)-…….,

Match the following columns:

The correct answer is:

(a)-……., (b)-……., (c)-……., (d)-…….,

Let Find p(-2).

Find the remainder when p (x) = 4x³ + 8x² – 17x + 10 is divided by (2x – 1).

If (x – 2) is a factor of 2x³ – 7x² + 11x + 5a, find the value of a.

For what value of m, p(x) = (x³ – 2mx² + 16) is divisible by (x + 2)?

If (a + b + c) = 8 and (ab + bc + ca) = 19, find (a² + b² + c²)

Expand: (3a + 4b + 5c)².

Expand: (3x + 2)².

Evaluate: {(28)³ + (-15)³ + (-13)³}.

If (x⁶⁰ + 60) is divided by (x + 1), the remainder is

One of the factors of (36x² – 1) + (1 + 6x)² is

If then (a³ – b³) = ?

The coefficient of x in the expansion of (x + 5)³ is

is a polynomial of degree

One of the zeroes of the polynomial 2x² + 7x – 4 is

Zero of the zero polynomial is

If (x + 1) and (x – 1) are factors of p (x) = ax³ + x² – 2x + b, find the values of a and b.

If (x + 2) is a factor of p (x) = ax³ + bx² + x – 6 and p(x) when divided by (x – 2) leaves a remainder 4, prove that a = 0 and b = 2.

The expanded form of (3x – 5)³ is

If a + b + c = 5 and ab + bc + ca = 10, prove that a³ + b³ + c³ – 3abc = – 25.

If p (x) = 2x³ + ax² + 3x – 5 and q (x) = x³ + x² – 4x + a leave the same remainder when divided by (x – 2), show that