Polynomials question paper

 

π Mark

Mathematics Test Polynomials

Class-9

Marks:-50                               Time:-60min

1. Multiple choice questions. (1x10=10)

a. which of the following expression is a polynomial ?

(i)x^1/2 -1 (ii)x-1/x-2 (iii)x²-(2/x²)+5 (iv)x²+ (2x^3/2/√x) +6

b. which of the following is quadratic polynomial ?

(i)x+4 (ii)(x+1)(x³-1)/(x²+1+x) (iii)x²+1/x (iv)x³+6

c. which of the following is binomial with degree 1 

(i)x²+x+3 (ii)x²+4 (iii)x (iv)2x-1-x

d. which is constant polynomial?

(i)x²+3 (ii)x² (iii)x (iv)x-1-x

e. what is the degree of π ?

(i) 1 (ii) 2 (iii) 3 (iv) 0

f. what is the degree of 0 ?

(i) 1 (ii) 2 (iii) not define (iv) 0

g. If (x⁴¹+41) is divisible by (x+1) then remainder is ?

(i) 1 (ii) 40 (iii) 0 (iv) 42

h. if p(x)=5x-4x²+3 then find p(-1 )= ?

(i)2 (ii) -2 (iii) 6 (iv) -6

I. if (2x-3) is a factor of (x+2x³-kx²+12) then k is

(i)0 (ii) 6 (iii)7 (iv) 9

j. if( 2x³-11x²-4x+5)(11x+2 )is polynomial then degree of this is

    (i)1 (ii) 2 (iii) 3 (iv) 4

2. Short type questions (3x10=30)

a. write the coefficient of x2 in each of the following.

(i)(x-1)(3x-4) (ii) (2x³-x+4)(4x²-3)

(iii) (πx²-x)(x-2)

b. Determine the degree of each polynomial .

(i)(2x-3)(7x-2) (ii) (x³+4)(4x²-3)

(iii) (πx²-x)(x²-2)

c. write the one example of each of them.

(I) monomial (ii)binomial (iii)trinomial

d. write the one example of each of them.

(I) linear polynomial (ii)constant polynomial

(iii) biquadratic polynomial

e. check whether 2 is the zero of the given polynomials

(i)x+2 (ii)x-2 (iii) x³-2x-4

f. if p(x)=x³+2x²-3x+4 then find

(i)p(-2) (ii)p(√3) (iii)p(1)

g. if -1 and 2 are the zeros of the polynomial p(x)=2x³-5x²+ax+b

then find the value of a and b.

h. Using remainder theorem , find the remainder , when p(x) is divisible

by g(x).

P(x)=x³-ax²+6x-a g(x)=x-a

I. Use factor theorem to show that x⁴+2x³-2x²+2x-3 is exactly divisible

by (x+3).

j. if (x+2)and (x-1) are the factors of polynomial p(x)=x³+10x²+mx+n

then find the value m and n.

3. Long type questions.

a. By using long division method find quotient and remainder

when p(x)=x⁴+1 is divided by g(x)=x-1.

b. what must be added to 2x⁴-5x³+2x²-x-3 so that the result is exactly

divisible by (x-2).