CLASSIFYING POLYNOMIALS DEGREE AND COEFFICIENT OF TERMS WORKSHEET
Question 1 :
State which of the following expressions are polynomials in one variable or not. Give reasons for your answer.
(i) 2x5-x3+x-6
(ii) 3x2-2x+1
(iii) y3+2√3
(iv) x - 1/x
(v) ∛t+2t
(vi) x3 + y3 +z6
Question 2 :
Write the coefficient of x2 and x in each of the following:
(i) 2+3x-4x2+x3
(ii) √3x + 1
(iii) x3 + √2x2+ 4x-1
(iv) 1/3 x² +x+6
Question 3 :
Write the degree of each of the following polynomials.
(i) 4- 3x2
(ii) 5y+√2
(iii) 12-x+4x³
(iv) 5
Question 4 :
Classify the following polynomials based on their degree.
(i) 3x2 + 2x +1
(ii) 4x3 -1
(iii) y+3
(iv) y2-4
(v) 4x3
(vi) 2x
Question 5 :
Give one example of a binomial of degree 27 and monomial of degree 49 and trinomial of degree 36.
(1) Solution :
State which of the following expressions are polynomials in one variable or not. Give reasons for your answer.
|
(i) 2x5-x3+x-6 (ii) 3x2-2x+1 (iii) y3+2√3 (iv) x - 1/x |
(i) Polynomial in one variable (ii) Polynomial in one variable (iii) Polynomial in one variable. (iv) Since the exponent of x is not a whole number, it is not a polynomial. |
(v) ∛t+2t
Since the exponent of t is not a whole number, it is not a polynomial.
(vi) x3 + y3 +z6
Not a polynomial in one variable.
(2) Solution :
|
Polynomial 2+3x-4x2+x3 √3x+1 x3+√2x2+4x-1 1/3 x²+x+6 |
Coefficient of x2 -4 0 √2 1/3 |
Coefficient of x 3 √3 4 x |
(3) Solution :
|
Polynomial (i) 4- 3x2 (ii) 5y+√2 (iii) 12-x+4x³ (iv) 5 |
Degree 2 1 3 0 |
(4) Solution :
(i) 3x2 + 2x +1
Since the degree of the polynomial is 2, it is a quadratic equation(polynomial).
(ii) 4x3-1
Since the degree of the polynomial is 3, it is a cubic equation(polynomial).
(iii) y+3
Since the degree of the polynomial is 1, it is a linear polynomial.
(iv) y2 - 4
Since the degree of the polynomial is 2, it is a quadratic polynomial.
(v) 4x3
Since the degree of the polynomial is 3, it is a cubic polynomial.
(vi) 2x
Since the degree of the polynomial is 1, it is a linear polynomial.
(5) Solution :
Give one example of a binomial of degree 27 and monomial of degree 49 and trinomial of degree 36.
- Binomial of degree 27 = ax27+b
- Monomial of degree 49 = cy49
- Trinomial of degree 36 = ax36+ bx6 + cx
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