Homework Practice

Homework Practice

Printable assignment

Polynomials Final Assessment

Section A: Core Concepts

Question 1mcq

The polynomial

9

has degree:

A.

0

B.

1

C.

9

D.undefined in Grade 10 polynomial classification

Question 2mcq

If

p(-1)=0

, then

-1

is:

A.the degree of

p(x)

B.a zero of

p(x)

C.the coefficient of

p(x)

D.the constant term

Question 3mcq

Find the zero of

5x+20

.

A.

4

B.

20

C.

-4

D.

5

Question 4mcq

A graph cuts the

x

-axis at

x=1

. What does this mean?

A.

p(1)=1

B.

1

is the degree.

C.The polynomial is constant.

D.

1

is a zero of the polynomial.

Question 5mcq

A line graph intersects the

x

-axis once. How many real zeros does it show?

A.

0

B.

1

C.

2

D.infinitely many

Question 6mcq

Find the zeros of

x^2+x-20

.

A.

-4

and

5

B.

2

and

10

C.

-2

and

-10

D.

4

and

-5

Section B: Skill Practice

Question 7mcq

Find the zeros of

x^2-9

.

A.

3

and

-3

B.

9

and

-9

C.

0

and

9

D.

3

only

Question 8mcq

For

x^2+8x+15

, the sum of zeros is:

A.

8

B.

15

C.

-8

D.

-15

Question 9mcq

For

2x^2-3x-5

, the product of zeros is:

A.

\fracrac{5}{2}

B.

\fracrac{3}{2}

C.

-\fracrac{3}{2}

D.

-\fracrac{5}{2}

Question 10mcq

Zeros of

2x^2-5x+2

are

\fracrac12

and

2

. Which is correct?

A.Sum

=\fracrac52

, product

=1

B.Sum

=1

, product

=\fracrac52

C.Sum

=-\fracrac52

, product

=-1

D.Sum

=2

, product

=\fracrac12

Question 11mcq

Form a monic quadratic polynomial with zeros

-3

and

7

.

A.

x^2+4x-21

B.

x^2-10x+21

C.

x^2-4x-21

D.

x^2+10x+21

Question 12mcq

Which polynomial has the same zeros as

2x^2+x-3

?

A.

2x^2+x+3

B.

4x^2+2x-6

C.

x^2+x-3

D.

4x^2+x-6

Section C: Application and Reasoning

Question 13mcq

If

2

is a zero of

x^2+ax-6

, find

a

.

A.

1

B.

-1

C.

2

D.

-2

Question 14mcq

A student says sum of zeros of

3x^2-6x+4

is

\fracrac{4}{3}

. What is wrong?

A.They forgot to divide by

a

for product.

B.They used

\fracrac{c}{a}

instead of

-\fracrac{b}{a}

.

C.They made no mistake.

D.The polynomial is linear.

Question 15mcq

Table:

x=-2,-1,0,1,2

and

p(x)=6,0,-2,0,6

. Which zeros are shown?

A.

0

and

2

B.

-2

and

2

C.

-1

and

1

D.

0

only

Question 16mcq

A quadratic graph just touches the

x

-axis at one point. Which statement is correct?

A.It has no real zero.

B.It has two distinct real zeros.

C.It has three real zeros.

D.It has one distinct real zero.

Question 17mcq

If zeros of

5x^2+kx+1

have sum

-3

, find

k

.

A.

-15

B.

15

C.

3

D.

-3

Question 18mcq

If zeros of

kx^2+7x+6

have product

2

, find

k

.

A.

12

B.

\fracrac13

C.

6

D.

3

Section D: Mixed Challenge

Question 19mcq

Which quadratic has zeros

\fracrac{2}{3}

and

-1

?

A.

3x^2+x-2

B.

3x^2-x-2

C.

3x^2+5x+2

D.

x^2+x-2

Question 20mcq

A polynomial

p(x)=x^2-6x+8

has zeros

2,4

. Which relation diagnoses both zeros correctly?

A.

2+4=-6

and

2\timesimes4=-8

B.

2-4=6

and

2+4=8

C.

2+4=6

and

2\timesimes4=8

D.

2\timesimes4=6

and

2+4=8

Question 21mcq

A quadratic polynomial has sum of zeros

-2

and product

-15

. Which is a monic polynomial?

A.

x^2-2x-15

B.

x^2+15x-2

C.

x^2-15x+2

D.

x^2+2x-15

Question 22mcq

Why do

p(x)

and

-5p(x)

have the same zeros?

A.Multiplying by

-5

does not change where

p(x)=0

.

B.Negative multiplication changes every zero.

C.Only positive multiples keep zeros.

D.They have same zeros only if

p(x)

is linear.

Question 23mcq

If one zero of

2x^2+px-15

is

3

, find the other zero and

p

.

A.Other zero

=\fracrac52

and

p=1

B.Other zero

=-5

and

p=4

C.Other zero

=-\fracrac{5}{2}

and

p=-1

D.Other zero

=5

and

p=-16

Question 24mcq

Assertion: For

ax^2+bx+c

, sum of zeros is

-\fracrac{b}{a}

. Reason: Product of zeros is

\fracrac{c}{a}

.

A.Both are true, and reason explains assertion.

B.Both are true, but the reason does not explain the assertion.

C.Assertion true, reason false.

D.Assertion false, reason true.