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Polynomials Worksheet

Polynomials Worksheet
  • Page 1
 1.  
Which expression is equivalent to (2x4y5)5?
a.
64x20y25
b.
32x20y25
c.
64x20y5
d.
32x20y5


Solution:

(2x4y5)5

= 25(x4)5(y5)5
[(abc)n = an × bn × cn.]

= 32x20y25
[(am)n = amn.]


Correct answer : (2)
 2.  
Which expression is equivalent to (7x3y2)37xy3?
a.
7xy3
b.
49x8y3
c.
4x3y
d.
4y3


Solution:

(7x3y2)37xy3

= 73(x3)3(y2)37xy3
[(abc)n = an × bn × cn.]

= 73x9y67xy3
[(am)n = amn.]

= 73 - 1 × x9 - 1 × y6 - 3
[aman = am - n.]

= 49x8y3


Correct answer : (2)
 3.  
Which of the following is a simplified expression for 4x - 12x2 - 5x + 6?
a.
3x - 3
b.
4x - 2
c.
xx + 3
d.
3x + 2


Solution:

4x - 12x2 - 5x + 6

= 4(x - 3)(x - 2)(x - 3)

= 4(x - 2)


Correct answer : (2)
 4.  
Simplify:
51x5y817x3y11
a.
7yx2
b.
3x2y3
c.
6yx3
d.
7yx3


Solution:

51x5y817x3y11

= 5117 × x5x3 × y8y11

= 3 × x5 - 3 × y8 - 11
[aman = am - n.]

= 3 × x2 × y- 3

= 3x2y3
[a- n = 1an.]


Correct answer : (2)
 5.  
Which of the following is equivalent to - 3n2(- 2n4 - 7n2)?
a.
6n6 - 21n4
b.
6n6 + 21n4
c.
- 6n6 - 21n4
d.
- 6n6 + 21n4


Solution:

- 3n2(- 2n4 - 7n2)

= (- 3n2)(- 2n4) - (- 3n2)(7n2)

= 6n4 + 2 + 21n2 + 2
[am × an = am + n.]

= 6n6 + 21n4


Correct answer : (2)
 6.  
Which of the algebra tiles represent the standard form of polynomials?

a.
Figure 1
b.
Figure 2
c.
Figure 3
d.
Figure 4


Solution:

Standard form means the exponents of the variable x must be in a descending order.

Figure1 represents the exponents of the variable x in the order 2, 0 and 1.

Figure 2 represents the exponents of the variable x in the order 1, 2 and 0.

Figure 3 represents the exponents of the variable x in the order 0, 2 and 1.

Figure 4 represents the exponents of the variable x in the order 2,1 and 0.

So, figure 4 represents the standard form of the polynomials.


Correct answer : (4)
 7.  
Which of the following model represents the polynomial expression 4x2 - 4x - 2?


a.
Figure 1
b.
Figure 2
c.
Figure 3
d.
None of the above


Solution:

4x2 - 4x - 2
[Original polynomial expression.]

The model must have four x2 tiles, four -x tiles and a constant -2.

Since the model in figure 3 has four x2 tiles, four -x tiles and a constant 2, figure 3 represents the polynomial expression 4x2 - 4x - 2.


Correct answer : (3)
 8.  
Simplify the polynomial expression 3x2 + x - 2x2 - 2x, using tiles.
a.
x2 + x
b.
2x2 + x
c.
x2 - x
d.
x2 + 2x


Solution:

3x2 + x - 2x2 - 2x
[Original polynomial expression.]


[Model each term in the expression using tiles.]


Group the tiles of the same size together and form zero pairs.


Remove the zero pairs and write the resultant expression.

The simplified polynomial expression is x2 - x.


Correct answer : (3)
 9.  
Write the simplified expression for the model shown.

a.
-2x2 + x + 1
b.
- 2x2 + 5x + 4
c.
4x2 + x - 1
d.
None of the above


Solution:


Group the tiles of the same size and same color together.


Remove the zero pairs and write the expression for the resultant.

The resultant polynomial expression is -2x2 + 5x + 4.


Correct answer : (2)
 10.  
Which of the algebra tiles does not represent the standard form?

a.
Figure 1
b.
Figure 4
c.
Figure 2
d.
Figure 3


Solution:

The polynomial will be in standard form, if the exponents of the variable x are in descending order.

In Figure 1, the order of the exponents of the variable x is 2, 0, 1, which is not a descending order.
[Descending order will have numbers ordered from the greatest to the least.]

In Figures 2, 3 and 4, the order of the exponents of the variable x is 2, 1 and 0, which is a descending order.

So, figure 1 does not represent the standard form of polynomial.


Correct answer : (1)

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