# Polynomial Worksheet

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**Q.1 Classify the following as monomials, binomials and trinomials :**

a)x

^{3}

b) 2y

^{2}– 4y + 3

c) t

^{2 }– 4

d) √2

e) x

^{3}+ 4x

^{2}+ 5x

f) u

^{7}+ u

^{2}– 4.

**Q.2 Write the coefficients of x**

^{2}in each of the following :a) 3x

^{2 }– 4y

b) x + x

^{2}+ 7y

c) 3x + 4y – 5z

d) x

^{2 }+ 2xy + 3y

^{2 }

**Q.3 Write the degree each of the following :**

a) 5x

^{3}+ 4x

^{2}+ 7x

b) 4 – y

^{2}

c) 5t – 3

**Q.4. Classify the following as linear, quadratic and cubic polynomials :**

a) x

^{2}+ x

b) x – x

^{3}

c) y + y

^{2}+ 4

d) 1 + x

e) 3t

f) r

^{2}

**Q.5 Find the value of the polynomial 5x – 4x**

^{2 }+ 3 at :a) x = 0 b) x = - 1 c) x = 2

**Q.6 Find the value of each of the following polynomials at indicated value of variables :**

a) p(x) = 5x

^{2}– 3x + 7 at x = 1

b) p(y) = 3y

^{3}– 4y + 4 at y = 2

c) p(t) = 4t

^{4 }+ 5y

^{3}– t

^{2}+ 6 at t = a

**Q.7**Check whether – 2 and 2 are zeroes of the polynomial x + 2 .

**Q.8**Find the zero of the polynomial p(x) = 2x + 1.

**Q.9**Verify whether 2 and - 2 are zero of the polynomial x

^{2}– 4 .

**Q.10**Verify whether 2 and 0 are zero of the polynomial x

^{2}– 2x .

**Q.11**Find the value of the following :

a) (3x

^{2}– 3x + 1)(x – 1) when x = 3

b) (3x

^{2}– 1)(4x

^{3}– 4x – 3) when x = - 1.

**Q.12 Evaluate the following for given values of the variables :**(polynomial worksheet)

a) x

^{4}– x

^{3}+ x

^{2}– x + 1 for x = 2

b) x

^{3}+ x

^{2}+ x + 1 for x = - 1.

**Q.13 Find the remainder and quotient in each of the following :**

a) Divide x

^{4}– 1 by x – 1 .

b) Divide x

^{3}– 3x

^{2 }+ 5x – 8 by x – 2.

**Q.14**Find the remainder when 4x

^{3}– 3x

^{2}+ 2x – 4 is divided by :

a) x – 1 b) x – 2 c) x + 1

d) x – 4 e) x + 2

**Q.15. Using remainder theorem, find the remainder :**

a) Divide x

^{6}– 1 by x – 1

b) Divide x

^{3}+ 1 by x + 1 .

**Q.16**Find the remainder when x

^{4}+ x

^{3}– 2x

^{2 }+ x + 1 is divided by x + 1.

**Q.17 If x – 2 is a factor of each of the following polynomials, then find the value of a in each case :**(polynomial worksheet)

a) x

^{2}– 3x + 5a

b) x

^{3}– 2ax

^{2}+ ax – 1

c) x

^{5}– 3x

^{4}– ax

^{3}+ 3ax

^{2}+ 2ax + 4.

**Polynomial Worksheet**

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