Free Printable Math of Legends Factoring Polynomials

1.

What is the first question you ask yourself when factoring a polynomial?

a)

How many terms does it have?

b)

Is there a GCF?

c)

What strategy should I use?

d)

Why do I have to learn this?!?!?!

2.

Factor:
56a³-8a

a)

8a²(56a³-8a)

b)

8a(7a²-1)

c)

8a(7a³-a)

d)

8a²(35a²-a)

3.

Factor:
2n²-8n³

a)

2n²(n-4n²)

b)

2n²(1-4n)

c)

2n³(10-8n²)

d)

3n(1-4n)

4.

Factor:
x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

5.

Factor:
x² - 10x + 24

a)

(x - 6)(x - 4)

b)

(x + 6)(x + 4)

c)

(x - 12)(x + 2)

d)

(x - 8)(x - 3)

6.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

7.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

8.

Factor Completely:

2c² + 2c - 84

Hint: Factor GCF first.

a)

(c-6)(2c+14)

b)

(c+7)(2x-12)

c)

(c-4)(2c+21)

d)

2(c+7)(c-6)

9.

Factor Completely:
3x² + 18x +15
Hint: Factor GCF first.

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

10.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

11.

Factor:
p² - 14p

a)

p(1 - 14)

b)

2p(p - 7)

c)

p²(1-14)

d)

p(p - 14)

12.

Factor
4n²-17n-15

a)

(n-10)(6n+1)

b)

(4n-5)(n-3)

c)

(n-5)(4n-3)

d)

(n-5)(4n+3)

13.

Factor
4n²-17n-15

a)

(n-10)(6n+1)

b)

(4n-5)(n-3)

c)

(n-5)(4n-3)

d)

(n-5)(4n+3)

14.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

15.

Divide: (p²+ 15p +56) ÷ (p +7)

a)

(p+7)

b)

(p+7)(p+8)

c)

(p + 8)

16.

Which of the following is one of the factors of the expression: $4x^2-25?$

a)

$\left(4x-5_{ }\right)$

b)

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

c)

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

d)

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

17.

What is the factored form of the expression? $x^2-16$

a)

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

b)

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

c)

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

d)

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

18.

Which shows the polynomial $8x^2+16x+8$ completely factored?

a)

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

b)

$\left(4x+4\right)\left(2x+2\right)$

c)

$8\left(x+1\right)^2$

d)

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

19.

When factored completely, $x^3-9x$ is equivalent to:

a)

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

b)

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

c)

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

d)

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

20.

Which expression is the factored form of $2x^2-2x-12?$

a)

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

b)

$2\left(x+6\right)\left(x-1\right)$

c)

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

d)

$2\left(x+1\right)\left(x-6\right)$

21.

If $\left(x-3\right)$ and $\left(x+7\right)$ are the factors of the trinomial $x^2+bx-21$ , what is the value of b?

a)

$-3$

b)

$-4$

c)

$7$

d)

$4$

22.

If $\left(2x-3\right)$ and $\left(x+5\right)$ are multiplied to form the trinomial $ax^2+bx+c$ , what is the value of b?

a)

$-15$

b)

$2$

c)

$7$

d)

$4$

23.

Factor the trinomial completely. $x^2-x-30$

a)

$\left(x+1\right)\left(x-30\right)$

b)

$\left(x+5\right)\left(x-6\right)$

c)

$\left(x+6\right)\left(x-5\right)$

d)

$prime$

24.

Factor the trinomial completely. $x^2-6x-72$

a)

$\left(x-12\right)\left(x+6\right)$

b)

$\left(x-72\right)\left(x+1\right)$

c)

$\left(x+12\right)\left(x-6\right)$

d)

$prime$

25.

Factor the binomial completely. $36-25x^2$

a)

$\left(6-5x\right)^2$

b)

$\left(6+5x\right)^2$

c)

$\left(6+5x\right)\left(6-5x\right)$

d)

$prime$

26.

What is the factored form of the expression? $x^2+x-6$

a)

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

b)

$\left(x+1\right)\left(x-6\right)$

c)

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

d)

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

27.

What are the binomial factors of $x^2+7x-18$

(Pick 2 answers)

a)

$\left(x-9\right)$

b)

$\left(x+9\right)$

c)

$\left(x-2\right)$

d)

$\left(x+2\right)$

28.

Which is a factor of $x^2-11x+24?$

a)

$\left(x+3\right)$

b)

$\left(x-3\right)$

c)

$\left(x+4\right)$

d)

$\left(x-4\right)$

29.

If $\left(x-3\right)$ is a factor of $x^2+x-12$ , then the other factor is?

a)

$\left(4x-3\right)$

b)

$\left(3x-4\right)$

c)

$\left(x-4\right)$

d)

$\left(x+4\right)$

30.

Written in factored form, the trinomial $2y^2+26y+80$ is equivalent to:

a)

$2\left(y-5\right)\left(y-8\right)$

b)

$\left(2y+5\right)\left(y+8\right)$

c)

$2\left(y+5\right)\left(y+8\right)$

d)

$\left(y+5\right)\left(2y+16\right)$

31.

Which of the following is the factor of a² - 2a³ + 2a⁴ ?

a)

a ( 1 - 2a + 2a²)

b)

a² ( 2a + 2a²)

c)

a² ( 1 - 2a + 2a²)

d)

None of the above

32.

Factor x² + xy

a)

x + y

b)

x²(x + y)

c)

x ( x² + y )

d)

x ( x + y )

33.

Which of the following is equal to ( x + 3) (x + 2) ?

a)

x² + 5x + 6

b)

x² - 5x - 6

c)

x²+ 5x - 6

d)

x² + 6x + 5

34.

Which of the following is equal to (x + 3) ( x - 5)?

a)

x² + 2x - 15

b)

x² - 2x + 15

c)

x² - 2x - 15

d)

x² + 2x + 15

35.

Factor x² + 19x + 84

a)

( x - 7 ) ( x - 12 )

b)

( x + 7) ( x + 12)

c)

( x + 8 ) ( x + 11 )

d)

( x - 8 ) ( x - 11 )

36.

Factor x² - 9x + 20

a)

( x - 5 ) ( x + 4 )

b)

( x - 5 ) ( x - 4 )

c)

( x - 10 ) (x - 2 )

d)

(x - 10 ) (x + 2 )

37.

( a - 4) + ( a - 4 ) 2x = ?

a)

(a - 4 ) 2x

b)

(a - 4) (2x - 4)

c)

( a - 4 )( 1 - 2 x )

d)

( a - 4 ) ( 1 + 2x )

38.

6x ( y - 2 ) + ( y - 2 )

a)

(6x - 1) ( y - 2 )

b)

(6x + 1 ) (y - 2 )

c)

(y - 2) (6x)

d)

(y - 2 ) ( 6x - 1)

39.

ab² - cb² - 6a + 6c = ?

a)

(b² - 6) (a + c )

b)

( b² + 6) ( a - c)

c)

(a - c ) (b - 6)

d)

(a - c) (b² - 6 )

40.

axy + bcxy - az - bcz = ?

a)

(a + bc) (xy - z)

b)

(a - bc) (xy - z)

c)

(a - bc) (xy + z)

d)

(a + bc) (xy + z)

41.

What is the greatest common factor of 3 and 6?

a)

3

b)

6

c)

9

d)

12

42.

Factor completely : 4x + 8

a)

2 (2x + 4)

b)

4 (x + 2)

c)

2 (2x - 4)

d)

4 (x - 2)

43.

(s – 5)² is equal to _______________.

a)

s² – 10 x + 25

b)

s² + 10 x + 25

c)

s² – 10 x - 25

d)

s² + 10 x – 25

44.

If $6x^2y^4$ is one of the factor of $24x^3y^{4^{ }}-\ 18x^2y^5\ what\ is\ the\ other\ factor?$

a)

$\left(4x\ +\ 3y\right)$

b)

$\left(4x\ -\ 3y\right)$

c)

$\left(-4x\ +\ 3y\right)$

d)

$\left(-4x\ -\ 3y\right)$

45.

Find the factors of the given expression m⁴n⁸ – 169.

a)

(mn – 13) (mn – 13)

b)

(mn + 13) (mn + 13)

c)

(m²n⁴ – 13) (m²n⁴ – 13)

d)

(m²n⁴ – 13) ((m²n⁴ + 13)

46.

Factor the expression $125x^3\ -\ 8y^3$ completely.

a)

$\left(5x\ +8y\right)\left(25x^2\ +\ 80xy\ +\ 64y^2\right)$

b)

$\left(5x\ -\ 8y\right)\left(25x^2\ +80xy\ -\ 64y^2\right)$

c)

$\left(5x\ -\ 8y\right)\left(25x^2\ -\ 80xy\ +\ 64y^2\right)$

d)

$\left(5x\ +\ 8y\right)\left(25x^2\ -80xy\ +\ 64y^2\right)$

47.

What is the missing term in the expression x² - ____ + 144 to make it a perfect square trinomial?

a)

12x

b)

24x

c)

36x

d)

28x

48.

One of the factors of 2a² + 5a – 12 is a + 4. What is the other factor?

a)

2a – 3

b)

2a + 3

c)

2a – 8

d)

2a + 8

49.

Find the greatest common monomial factor of 25x² + 15x.

a)

5x

b)

x

c)

10x

d)

10

50.

What are the factors of the expression 16m² + 8m?

a)

(8m + 1) (2m + 4)

b)

(4m + 4) (4m + 2)

c)

(8m) (2m + 1)

d)

(4m) (4m + 2)

Math of Legends Factoring Polynomials

Total questions: 50

Worksheet time: 34mins

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