Free Printable Exponents, Polynomials, & Factoring

1.

Factor completely:

10x² + 15x - 5

a)

25(10x³+45x-15)

b)

5(2x³ + 3x²-x)

c)

x(10x³+15x-5)

d)

5(2x²+3x-1)

2.

Factor completely:

4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

3.

Factor completely:

5k³ + 7k² + k

a)

5k(k² +2k + 1)

b)

7k(5k² +k + 1)

c)

k(5k² + 7k + 1)

d)

5k³ + 7k² + k

4.

Factor completely:

56a³-8a

a)

8a²(56a³-8a)

b)

8a(7a²-1)

c)

8a(7a³-a)

d)

8a²(35a²-a)

5.

Factor completely:

8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

6.

Factor completely:

x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

7.

Factor completely:

x² + 14x + 24

a)

(x + 6)(x + 4)

b)

(x + 10)(x + 2)

c)

(x + 8)(x + 3)

d)

(x + 2)(x + 12)

8.

Factor Completely: 5x²-11x+6

a)

(5x+6)(x-1)

b)

(5x-6)(x-1)

c)

(2x-7)(x-3)

d)

(5x-6)(x+1)

9.

Factor completely:

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

10.

Factor completely:

5m² - 45m + 90

a)

3(m + 1)(m + 8)

b)

5(m - 3)(m - 6)

c)

2(m - 7)(m + 3)

d)

5(m - 5)(m + 3)

11.

Factor completely:

8r³ - 16r²

a)

4r²(2r - 4)

b)

8r²(r - 2)

c)

8(r³ - r²)

d)

4(r³ - 2r²)

12.

Factor by grouping
x³ - 4x² -4x + 16

a)

(x+4)(x+2)

b)

(x-4)(x-2)(x+2)

c)

(x+4)(x-2)(x+2)

d)

(x-4)(x-2)

13.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

14.

Factor completely:

30x³+15x²-18x-9

a)

(5x²-3)(6x+1)

b)

(5x²-3)(6x+3)

c)

3(5x²+3)(2x-1)

d)

3(5x²-3)(2x+1)

15.

Factor $32x^3+148x^2-60x$

a)

$32\left(x+5\right)\left(x+3\right)$

b)

$4\left(8x+15\right)\left(x-1\right)$

c)

$4x\left(4x+3\right)\left(2x-5\right)$

d)

$4x\left(x+5\right)\left(8x-3\right)$

16.

Factor $36v^3-36v^2+8v$

a)

$4v\left(3v-1\right)\left(3v-2\right)$

b)

$2\left(3v+5\right)\left(2v-7\right)$

c)

$4\left(3v+2\right)\left(3v+1\right)$

d)

$4v\left(9v+2\right)\left(v+1\right)$

17.

Factor $24m^2+18m-81$

a)

$3\left(4m+9\right)\left(2m-3\right)$

b)

Not Factorable

c)

$3\left(2m+3\right)\left(4m-9\right)$

d)

$3\left(2m+9\right)\left(4m+3\right)$

18.

Factor $16x^4-25y^2$

a)

$\left(4x^2+5y\right)\left(4x^2-5y\right)$

b)

$\left(-4x^2+5\right)\left(4x^2-5\right)$

c)

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

d)

$\left(4x^2-5y\right)^2$

19.

Factor $9a^4-12a^2+4$

a)

$\left(3a^2+2\right)\left(3a^2-2\right)$

b)

Not Factorable

c)

$\left(9a^2+4\right)^2$

d)

$\left(3a^2-2\right)^2$

20.

Factor $10b^2-65b-350$

a)

$2\left(b+7\right)\left(b-5\right)$

b)

$10\left(b+35\right)\left(b-1\right)$

c)

$5\left(2b+7\right)\left(b-10\right)$

d)

$10\left(b+5\right)\left(b-7\right)$

21.

Factor $28m^4-192m^3-28m^2$

a)

Not Factorable

b)

$4m^2\left(7m+1\right)\left(m-7\right)$

c)

$4m^2\left(7m+1\right)\left(m+7\right)$

d)

$4m^2\left(7m-1\right)\left(m+7\right)$

22.

Factor $6n^2-58n+36$

a)

$6\left(n+1\right)\left(n+6\right)$

b)

$n\left(3n-10\right)$

c)

$\left(5n+6\right)\left(n-8\right)$

d)

$2\left(3n-2\right)\left(n-9\right)$

23.

Factor $3m^2+11m-4$

a)

$\left(3m-1\right)\left(m-4\right)$

b)

$\left(3m+1\right)\left(m-4\right)$

c)

$\left(m-1\right)\left(3m+4\right)$

d)

$\left(3m-1\right)\left(m+4\right)$

24.

Factor $3k^3+15k^2-150k$

a)

$3k\left(k+50\right)\left(k-1\right)$

b)

$\left(k+10\right)\left(k-5\right)$

c)

$3k\left(k+10\right)\left(k+5\right)$

d)

$3k\left(k+10\right)\left(k-5\right)$

25.

Factor $-n^3-4n^2+12n$

a)

$-n\left(n-2\right)\left(n+6\right)$

b)

$-\left(n+2\right)\left(n+6\right)$

c)

$-n\left(n+2\right)\left(n-6\right)$

d)

Not Factorable

26.

Factor $25v^{6\ }-40v^3+16$

a)

$\left(5v^3+2\right)\left(5v^3-2\right)$

b)

$\left(5v^3-4\right)^2$

c)

$\left(25v^3+16\right)^2$

d)

$\left(3v^3+5\right)\left(3v^3-5\right)$

27.

Factor $25x^4-16$

a)

$\left(5x^2+8\right)^2$

b)

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

c)

$\left(5x^2+4\right)\left(5x^2-4\right)$

d)

$\left(x^2+1\right)^2$

28.

Factor $63x^{15}y-63x^{11}y+45x^{10}$

a)

$36x^{10}\left(7x^6y-7xy+10\right)$

b)

$9x^{10}\left(63x^6y-63x^2y+45x\right)$

c)

$9x^{10}\left(7x^5y-7xy+5\right)$

d)

$9x^{10}y\left(7x^5y-7xy+5y\right)$

29.

Which of the following are in the form of difference of squares? Select all that apply.

a)

(x - 3)(x + 3)

b)

(2d - 5)(2d - 5)

c)

(f + 6)(f - 6)

d)

(k² - 10)(k² + 10)

e)

(y + 1)(y + 1)

30.

Factor the expression completely:

25x^2+4

a)

Not Factorable

b)

$\left(5x-2\right)\left(5x+2\right)$

c)

$\left(5x-4\right)\left(5x-1\right)$

d)

$\left(5x+4\right)\left(5x+1\right)$

31.

Factor the expression completely:

45x^2-20

a)

$\left(5x+4\right)\left(9x-5\right)$

b)

$\left(3x-10\right)\left(15x+2\right)$

c)

$5\left(3x+2\right)\left(3x-2\right)$

d)

$5\left(9x-1\right)\left(x-4\right)$

32.

Simplify the expression:

\left(a^4b\right)^2\left(a^3b^2\right)^4

a)

$4a^8b$

b)

$a^{13}b^8$

c)

$-2a^8y^7$

d)

$a^{20}b^{10}$

33.

Simplify the expression: $\frac{12x^9y^4z^2}{24x^3y^4z^6}$

a)

$2x^3z^3$

b)

$\frac{x^6}{2z^4}$

c)

$\frac{x^3}{2z^3}$

d)

$\frac{2x^6}{x^4}$

34.

Simplify the expression:

$5x^9\cdot-6x^2$

a)

$-30x^{11}$

b)

$-30x^{18}$

c)

$-x^{11}$

d)

$-x^{18}$

35.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

36.

Simplify:

$\frac{x^6y^{-3}}{x^{-4}y^2}$

a)

$\frac{x^{10}}{y^5}$

b)

$\frac{x^2}{y^5}$

c)

$x^2y^5$

d)

$x^{10}y^5$

37.

Simplify:

$\left(2x^2y^4\right)^3$

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

38.

Simplify:

$\frac{12a^2b^8}{24a^4b^2}$

a)

$2a^2b^6$

b)

$\frac{a^2b^6}{2}$

c)

$\frac{b^6}{2a^2}$

d)

$\frac{2b^6}{a^2}$

39.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

40.

Simplify:

$\left(\frac{2vu^3}{u^2v^3\cdot u^3v^2}\right)^{-5}$

a)

$\frac{u^{10}v^{20}}{32}$

b)

$\frac{1}{v^3u^4}$

c)

$\frac{v^{35}}{u^{35}}$

d)

$\frac{u^{80}}{v^{62}}$

41.

Simplify:

$\frac{16a^{12}b^6}{4a^4b^{-3}}$

a)

$4a^3b^{-2}$

b)

$\frac{4a^3}{b^2}$

c)

$4a^8b^9$

d)

$4a^8b^3$

42.

Simplify: $\frac{a^{-16}}{a^{-4}}$

a)

$a^{-4}$

b)

$\frac{1}{a^{12}}$

c)

$a^4$

d)

$\frac{1}{a^{20}}$

43.

Simplify:

$\left(2a^4b^3\right)^5$

a)

$10a^{20}b^{15}$

b)

$7a^{20}b^{15}$

c)

$32a^9b^8$

d)

$32a^{20}b^{15}$

44.

Simplify: $3a^0$

a)

0

b)

1

c)

3

d)

31

45.

Simplify:

$\frac{8x^4y^5x^{-6}y^{-7}}{4x^2y^3x^{-4}y^{-5}}$

a)

$\frac{2}{x^4y^4}$

b)

$\frac{2x^4}{y^4}$

c)

2x⁴y⁴

d)

2

46.

Simplify:

$-\frac{8x^4y}{24x^9y^8}$

a)

$\frac{-1}{3x^5y^7}$

b)

$3x^5y^7$

c)

$16x^{13}y^9$

d)

$\frac{1}{16x^{13}y^9}$

47.

$\left(\frac{3m^2n^7}{m}\right)^5$

a)

$15m^7n^{12}$

b)

$243m^5n^{35}$

c)

$15m^{15}n^{35}$

d)

$243m^7n^{12}$

48.

$\frac{x^{-2}}{x^{-10}y^{-8}}$

a)

$\frac{x^8}{y^{-8}}$

b)

$x^{20}y^8$

c)

$x^8y^8$

d)

$\frac{x^{10}y^8}{x^2}$

49.

What is the area of the rectangle with the given sides?

a)

$7x^3y^8z^4$

b)

$10x^2y^{16}z^3$

c)

$10x^3y^8z^4$

d)

none of the above

50.

$\left(8x^3\right)\left(-7x^4y^3\right)$

a)

$\frac{8x^3}{7x^4y^3}$

b)

$x^7y^4$

c)

$-56x^7y^3$

d)

$\frac{8}{7xy^3}$

Exponents, Polynomials, & Factoring

Total questions: 50

Worksheet time: 2hrs 23mins

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