Polynomial Worksheet

This section is about polynomial worksheet.
Q.1 Classify the following as monomials, binomials and trinomials :
a)x³
b) 2y² – 4y + 3
c) t²– 4
d) √2
e) x³ + 4x ² + 5x
f) u⁷ + u² – 4.
Q.2 Write the coefficients of x² in each of the following :
a) 3x²– 4y
b) x + x²+ 7y
c) 3x + 4y – 5z
d) x²+ 2xy + 3y²
Q.3 Write the degree each of the following :
a) 5x³ + 4x² + 7x
b) 4 – y²
c) 5t – 3
Q.4. Classify the following as linear, quadratic and cubic polynomials :
a) x² + x
b) x – x³
c) y + y² + 4
d) 1 + x
e) 3t
f) r²
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) = 5x² – 3x + 7 at x = 1
b) p(y) = 3y³ – 4y + 4 at y = 2
c) p(t) = 4t⁴+ 5y³ – t² + 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 x² – 4 .
Q.10 Verify whether 2 and 0 are zero of the polynomial x² – 2x .
Q.11 Find the value of the following :
a) (3x² – 3x + 1)(x – 1) when x = 3
b) (3x² – 1)(4x³ – 4x – 3) when x = - 1.
Q.12 Evaluate the following for given values of the variables :(polynomial worksheet)
a) x⁴ – x³+ x² – x + 1 for x = 2
b) x³ + x² + x + 1 for x = - 1.
Q.13 Find the remainder and quotient in each of the following :
a) Divide x⁴ – 1 by x – 1 .
b) Divide x³ – 3x²+ 5x – 8 by x – 2.
Q.14 Find the remainder when 4x³ – 3x² + 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 x⁶ – 1 by x – 1
b) Divide x³ + 1 by x + 1 .
Q.16 Find the remainder when x⁴ + x³ – 2x²+ 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) x² – 3x + 5a
b) x³ – 2ax² + ax – 1
c) x⁵ – 3x⁴ – ax³+ 3ax² + 2ax + 4.

Polynomial Worksheet

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