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Polynomial exercise
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POLYNOMIALSQuestions carrying 1 mark:
1) x2-2x+1 is a polynomial in:a. One Variableb. Two Variablesc. Three variabled. None of the above
2) The coefficient of x2 in 3x3+2x2-x+1 is:a. 1b. 2c. 3d. -1
3) The degree of 4x3-12x2+3x+9 isa. 0b. 1c. 2d. 3
4) x2 – x is ________ polynomial.a. Linearb. Quadraticc. Cubicd. None of the above
5) x – x3 is a ________ polynomial.a. Linearb. Quadraticc. Cubicd. None of the above
6) 1+3x is a _________ polynomial.a. Linearb. Quadraticc. Cubicd. None of the above
7) A polynomial with one degree is called:a) Linear polynomialb) Quadratic polynomialc) Monomiald) Binomial
8) Degree of the polynomial 7x5 + 8x2 – 5x + 3 is:a) 1b) 3c) 2d) 5
9) What is the degree of a zero polynomial?a) 0b) 1c) Any natural numberd) Not defined
10) The polynomial with degree as 2 is called
a) Linear polynomialb) Quadratic polynomialc) Monomiald) Binomial
Questions carrying 2 marks:
1. Find the value of the polynomial 5x – 4x2 + 3 at x = 0
2. Find p (0) for y2 – y +1
3. Verify whether x = – 1 is zero of the polynomial p (x) = x2 – 1
4. Verify whether x= 2 is a zero of the polynomial p(x) = (x + 1)(x – 2)
5. Find the zero of the following polynomials: (a) p (x) = 2x + 5(b) p (x) = x – 5(c) p (x) = 3x – 2
6. Find the remainder when x3 – ax2 + 6x – a is divided by x – a.
7. Find the value of the polynomial 4x3-3x2-2x+1 at x = 0
8. If x + y + z = 0, show that x3 + y3 + z3 = 3 xyz.
Questions carrying 3 marks:
1. Check if (x + 1) is factor of p(x) = x4 + x3 + x2 + x + 1 using factor theorem
2. Check if (x – 1) is a factor of p(x) = x4 + 3x3 + 3x2 + x + 1 using factor theorem
3. Find the remainder when 3x2 + x -1 is divided by (x + 1) using remainder theorem
4. Find the remainder when x3 + x2 + x + 1 is divided by (x + 1) using remainder theorem
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