﻿ Polynomials Worksheet | Problems & Solutions

# Polynomials Worksheet

Polynomials Worksheet
• Page 1
1.
Which expression is equivalent to (2$x$4$y$5)5?
 a. 64$x$20$y$25 b. 32$x$20$y$25 c. 64$x$20$y$5 d. 32$x$20$y$5

#### Solution:

(2x4y5)5

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

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

2.
Which expression is equivalent to $\frac{{\left(7{x}^{3}{y}^{2}\right)}^{3}}{7x{y}^{3}}$?
 a. 7$x$$y$3 b. 49$x$8$y$3 c. $\frac{4{x}^{3}}{y}$ d. $\frac{4}{{y}^{3}}$

#### 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

3.
Which of the following is a simplified expression for ?
 a. b. c. d.

#### Solution:

4x - 12x2 - 5x + 6

= 4(x - 3)(x - 2)(x - 3)

= 4(x - 2)

4.
Simplify:
$\frac{51{x}^{5}{y}^{8}}{17{x}^{3}{y}^{11}}$
 a. $\frac{7y}{{x}^{2}}$ b. $\frac{3{x}^{2}}{{y}^{3}}$ c. $\frac{6y}{{x}^{3}}$ d. $\frac{7y}{{x}^{3}}$

#### Solution:

51x5y817x3y11

= 5117 × x5x3 × y8y11

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

= 3 × x2 × y- 3

= 3x2y3
[a- n = 1an.]

5.
Which of the following is equivalent to - 3$n$2(- 2$n$4 - 7$n$2)?
 a. 6${n}^{6}$ - 21${n}^{4}$ b. 6${n}^{6}$ + 21${n}^{4}$ c. - 6${n}^{6}$ - 21${n}^{4}$ d. - 6${n}^{6}$ + 21${n}^{4}$

#### Solution:

- 3n2(- 2n4 - 7n2)

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

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

= 6n6 + 21n4

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.

7.
Which of the following model represents the polynomial expression 4$x$2 - 4$x$ - 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.

8.
Simplify the polynomial expression 3$x$2 + $x$ - 2$x$2 - 2$x$, using tiles.
 a. $x$2 + $x$ b. 2$x$2 + $x$ c. $x$2 - $x$ d. $x$2 + 2$x$

#### 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.

9.
Write the simplified expression for the model shown.

 a. -2$x$2 + $x$ + 1 b. - 2$x$2 + 5$x$ + 4 c. 4$x$2 + $x$ - 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.

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.
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