Polynomial Worksheet

This section is about polynomial worksheet.
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 x2 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 – 4x2 + 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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