Free Printable Polynomial Quiz

1.

Identify the degree of:
2b⁸c²

a)

10

b)

8

c)

2

d)

16

2.

7. If P(x) = 2x ³ + 3x² – 11x + 6 , then find the value of P ( 1 )._____

a)

1

b)

2

c)

3

d)

0

3.

10. If product of the zeroes is one in quadratic polynomials then which of the following is correct ------------

a)

a=c

b)

a = b

c)

c= b

d)

a

4.

If one zero of the quadratic polynomial $x^2+3x+k$ is 2, then the value of $k$ is

a)

10

b)

$-\ 10$

c)

5

d)

$-\ 5$

5.

If 1 is a zero of the polynomial p(x) = ax²– 3(a – 1) x – 1, then find the value of a.

a)

1

b)

0

c)

2

d)

3

6.

The number of polynomials having zeroes as –2 and 5 is

a)

1

b)

2

c)

3

d)

more than 3

7.

The degree of the polynomial (x + 1)(x² – x – x⁴ +1) is:

a)

2

b)

3

c)

4

d)

5

8.

If the zeroes of the quadratic polynomial x² + (a + 1)x + b are 2 and –3, then

a)

a = –7, b = –1

b)

a = 5, b = –1

c)

a = 2, b = – 6

d)

a = 0, b = – 6

9.

If one of the zeroes of the quadratic polynomial (k – 1)x² + kx + 1 is –3, then the value of k is

a)

4/3

b)

-4/3

c)

2/3

d)

-2/3

10.

A real number 'α' is called zero of the polynomial f(x) if ____

a)

f(α) = -1

b)

f(α) = 0

c)

f(α) = 1

d)

None of the above

11.

The zeros of the quadratic polynomial x² +99x+127 are

a)

Both Positive

b)

Both Negative

c)

One Positive and one negative

d)

Both Equal

12.

6) Degree of

$a_0+a_1x+a_2x^2+a_3x^3+.......\ n\ terms$ is _______________

a)

0

b)

3

c)

n

d)

n-1

13.

10) Degree of

\left(x^2+2\right)\left(y^3-5\right)

is _____

a)

2

b)

3

c)

4

d)

5

14.

$Factorise:\ 40+3x-x^2$

a)

$\left(x-8\right)\left(x+5\right)$

b)

$\left(8-x\right)\left(x+5\right)$

c)

$\left(8-x\right)\left(5-x\right)$

d)

$\left(x+8\right)\left(x-5\right)$

15.

$Factorise:\ 6-x-x^2$

a)

$\left(x+3\right)\left(x+2\right)$

b)

$\left(x+3\right)\left(x-2\right)$

c)

$\left(3-x\right)\left(2+x\right)$

d)

$\left(3+x\right)\left(2-x\right)$

16.

The number of zeroes that polynomial f(x) = (x – 2)² + 4 can have is:

a)

1

b)

2

c)

0

d)

3

17.

Zeroes of a polynomial can be determined graphically. No. of real zeroes of a polynomial is equal to no. of points where the graph of polynomial

a)

intersects y-axis

b)

intersects x-axis

c)

intersects y-axis or intersects x-axis

d)

none of these

18.

If graph of a polynomial does not intersects the x-axis but intersects y-axis in one point, then no, of real zeroes of the polynomial is equal to

a)

0

b)

1

c)

0 or 1

d)

none of these

19.

If p(x) = a x ² + bx + c, and a + b + c = 0, then one zero is

a)

-1

b)

1

c)

-1/2

d)

1/2

20.

a)

4

b)

5

c)

3

d)

2

21.

a)

No Zero

b)

0

c)

5

d)

0 and 5

22.

a)

1

b)

3

c)

1 and 3

d)

2

23.

If $a^2+b^2+c^2-ab-bc-ca=0$ , then which of the following is correct?

a)

$a\ =\ b\ \ne\ c$

b)

$a\ \ne\ b\ \ne\ c$

c)

$a\ =b\ =c$

d)

$a\ \ne\ b\ =c$

24.

Factorise: $\left(x-y\right)^3+\left(y-z\right)^3+\left(z-x\right)^3$

a)

$\left(x-y\right)^3$

b)

$3\left(x-y\right)\left(y-z\right)\left(z-x\right)$

c)

$3\left(x-y\right)\left(y-z\right)\left(x-z\right)$

d)

$3xyz$

25.

How many real zeroes are there for $x^3+x^2+x-3$ ?

a)

2

b)

3

c)

1

d)

4

26.

The value of m for which x - 2 is a factor of the polynomial $x^4-x^3+2x^2-mx+4$

a)

-10

b)

4

c)

10

d)

9

27.

If a + b + c = 8 and ab + bc + ca = 20, find the value of $a^3+b^3+c^3-3abc$

a)

29

b)

34

c)

33

d)

32

28.

If one of the zeroes of a quadratic polynomial of the form x²+ax + b is the negative of the other, then it

a)

has no linear term and the constant term is negative.

b)

has no linear term and the constant term is positive.

c)

can have a linear term but the constant term is negative.

d)

can have a linear term but the constant term is positive.

29.

Can x – 1 be the remainder on division of a polynomial p (x) by 2x + 3?

a)

Yes

b)

No

30.

If p(x) = ax² + bx + c and a + c = b, then one of the zeroes is

a)

b/a

b)

c/a

c)

-b/a

d)

-c/a

31.

The graph of a polynomial p(x) passes through the points (-5, 0), (0, -40), (8, 0) and (5, -30). Which among the following is a factor of p(x)?

a)

$x-5$

b)

$x-8$

c)

$x+30$

d)

$x+40$

32.

Find the remainder when the polynomial $ax^3+bx^2+cx+d$ is divided by $ax+b$

a)

$ad-bc$

b)

$\frac{1}{a}\left(ad-bc\right)$

c)

$\frac{1}{d}\left(ad-bc\right)$

d)

$\frac{a+b+cd}{2}$

33.

If 2 and 3 are zeroes of the quadratic polynomial $x^2+ax+b,$ the values of $a+b$ is

a)

-3

b)

5

c)

1

d)

6

34.

The function f(x) = $x^3−6x^2+ax+b$ where a and b are constants is exactly divisible by (x – 3) and leaves a remainder of –55 when divided by (x + 2) Find the value of a + b

a)

-30

b)

10

c)

7

d)

13

35.

If (x – k) is the H.C.F. of $x^2+x-12$ and $2x^2-kx-9$ , then the value of k is

a)

-3

b)

3

c)

both (a) and (b)

d)

none

36.

If the polynomial $x^4+x^3+8x^2+ax+b$ is divisible by $x^2+1$ , then the value of $a+b$ is

a)

7

b)

4

c)

8

d)

3

37.

If $a+2b+3c=0$ , then $a^3+8b^3+27c^3$ is equal to

a)

9abc

b)

6abc

c)

21abc

d)

18abc

38.

The polynomials $p\left(x\right)=ax^3+3x^2−3$ and $f\left(x\right)=2x^3−5x+a$ when divided by $(x-4)$ leaves remainder $R_1\ \&\ R_2$ such that $2R_1-R_2=0$ , then the value of a is

a)

$-\frac{18}{127}$

b)

$\frac{18}{127}$

c)

$\frac{17}{127}$

d)

$\frac{127}{18}$

39.

Which of the following does NOT represent a zero polynomial?

a)

p(x) = 0

b)

$p(x)=x^0-1$

c)

$p(x)=x^0$

d)

$p(x)=0.x^0$

40.

If the zeroes of the quadratic polynomial $ax^2+bx+c,\ c\ne0$ are equal, then

a)

c and a have opposite signs

b)

c and b have same sign

c)

c and a have same sign

d)

c and b have opposite signs

Polynomial Quiz - I

Total questions: 40

Worksheet time: 20mins

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