Free Printable Factoring Trinomials ax^2

1.

Factor using GCF or monomial factoring:

2n²-8n³

a)

2n²(n-4n²)

b)

2n²(1-4n)

c)

2n³(10-8n²)

d)

3n(1-4n)

2.

What is the first step when factoring polynomials?

a)

Find the GCF

b)

List all the terms

c)

Make the X and fill in the top and bottom

d)

Multiply a and c

3.

What is the common monomial factor of $6x^3+3x^2-12x$ ?

a)

$3$

b)

$2x$

c)

$3x$

d)

$3x^2$

4.

The factored form of m²+ 6m + 5 is

(m+2)(m+ 3)

a)

true

b)

false

5.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

6.

factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

7.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

8.

Factor
a² - a - 12

a)

(a - 4)(a + 3)

b)

(a + 6)(a - 4)

c)

(a - 6)(a + 4)

d)

(a + 4)(a - 3)

9.

Which of the following is a factor of
r² -16r + 60 ?

a)

r + 6

b)

r + 10

c)

r - 6

d)

r -30

10.

Factor completely:
$r^2+r-6$

a)

$\left(r+2\right)\left(r+3\right)$

b)

$\left(r+4\right)\left(r-7\right)$

c)

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

d)

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

11.

Which of the following is a difference of perfect squares?

a)

x² - 18

b)

4x² + 36

c)

9x² - 100

d)

x² + 4

12.

If a trinomial, ax²+or- bx + c, has a positive "c" value, what do you know about the signs in its binomial factors?

a)

Both signs are positive.

b)

Both signs are negative.

c)

One sign is positive and one is negative.

d)

The signs are the same, both + or both -

13.

Factor by GCF:

18a²-15a

a)

15a(3a-1)

b)

3a(6a-1)

c)

3(6a-5)

d)

3a(6a-5)

14.

Factor:
x² - 9

a)

( x -9) (x - 9)

b)

(x + 3) (x + 3)

c)

(x + 3) (x - 3)

d)

( x + 9) (x-9)

15.

x²- 400

a)

( x - 200) ( x + 200)

b)

( x + 20) ( x + 20)

c)

Prime

d)

( x - 20) ( x + 20)

16.

Factoring reverses the process of what?

a)

Division

b)

Multiplication

c)

Addition

d)

Subtraction

17.

Factor
r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

18.

Which is another way of correctly expressing
(x - 3)(x - 3)?

a)

(x² - 3²)

b)

(x² - 3)

c)

(x + 3)(x - 3)

d)

(x - 3)²

19.

Factor:
x² - 49

a)

(x + 7)(x - 7)

b)

(x + 7)²

c)

(x - 7)²

d)

(x+7)(x-1)

20.

What is the GCF of the trinomial?
3x²- 9x -120

a)

3

b)

2

c)

6

d)

9

21.

Factor completely.
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

22.

Factor completely:
3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

23.

A rectangle has an area of 2x² – 19x +45 ft². What are the dimensions of the rectangle?

a)

(2x - 9)(x - 5)

b)

(2x + 9)(x + 5)

c)

(2x - 5)(x - 9)

d)

(2x - 5)(x + 9)

24.

If a trinomial, ax²+ bx + c, has a negative "c" value, what do you know about the signs in its binomial factors.

a)

The signs are both +.

b)

The signs are one + and one -

c)

The signs are both -

25.

Solve
x² + 20 = -9x

a)

x=-4
x=-5

b)

x=4
x=5

c)

x=2
x=10

d)

x=-4
x=5

26.

Factoring reverses the process of what?

a)

Division

b)

Multiplication

c)

Addition

d)

Subtraction

27.

Factor
r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

28.

Which is another way of correctly expressing
(x - 3)(x - 3)?

a)

(x² - 3²)

b)

(x² - 3)

c)

(x + 3)(x - 3)

d)

(x - 3)²

29.

Factor:
x² - 49

a)

(x + 7)(x - 7)

b)

(x + 7)²

c)

(x - 7)²

d)

(x+7)(x-1)

30.

What is the GCF of the trinomial?
3x²- 9x -120

a)

3

b)

2

c)

6

d)

9

31.

Factor completely.
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

32.

Factor completely:
3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

33.

A rectangle has an area of 2x² – 19x +45 ft². What are the dimensions of the rectangle?

a)

(2x - 9)(x - 5)

b)

(2x + 9)(x + 5)

c)

(2x - 5)(x - 9)

d)

(2x - 5)(x + 9)

34.

If a trinomial, ax²+ bx + c, has a negative "c" value, what do you know about the signs in its binomial factors.

a)

The signs are both +.

b)

The signs are one + and one -

c)

The signs are both -

35.

Solve
x² + 20 = -9x

a)

x=-4
x=-5

b)

x=4
x=5

c)

x=2
x=10

d)

x=-4
x=5

36.

Factor:
x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

37.

Factor:
x²- 16

a)

Prime

b)

( x - 4) ( x + 4)

c)

( x - 8) ( x + 8)

d)

( x - 4) ( x - 4)

38.

Factor:
x²- 16

a)

Prime

b)

( x - 4) ( x + 4)

c)

( x - 8) ( x + 8)

d)

( x - 4) ( x - 4)

39.

Factor:
x²- 225

a)

( x + 15) ( x + 15)

b)

Prime

c)

( x - 15) ( x + 15)

d)

( x - 15) ( x - 15)

40.

Factor:
x²- 400

a)

( x - 200) ( x + 200)

b)

( x + 20) ( x + 20)

c)

Prime

d)

( x - 20) ( x + 20)

41.

Factor:
x²- 169

a)

( x - 13) ( x + 13)

b)

( x + 13) ( x + 13)

c)

( x - 13) ( x -13)

d)

Prime

42.

Factor:
25x²- 100y²

a)

( 5x - 10y) (5xy + 10y)

b)

( 5x - 10y)²

c)

Prime

d)

( 5x - 50y) (5x + 50y)

43.

Factor:
3x²- 75

a)

3( x + 5 ) ( x - 5 )

b)

Prime

c)

( x + 5 ) ( x - 5 )

d)

3( x - 5 ) ( x - 5 )

44.

Factor:
x²+ 81

a)

Prime (not factorable)

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

45.

Which of the following trinomials is a perfect square trinomial?

a)

r² - 6r + 36

b)

4y² + 10y + 25

c)

x² + 16x + 16

d)

9a² - 12a + 4

46.

Factor:
x² - 30x + 225

a)

(x + 15)²

b)

(x - 15)²

c)

(x + 25)²

d)

(x - 25)²

47.

Factor, if possible: 4x²+36x+81

a)

(4x+81)²

b)

(2x+9)²

c)

Prime /
Not factorable.

d)

(2x-9)²

48.

Factor, if possible:
64x²-16x+1

a)

Not factorable.

b)

(32x-1)²

c)

(8x+1)²

d)

(8x-1)²

49.

a)

A

b)

B

c)

C

d)

D

50.

a)

A

b)

B

c)

C

d)

D

51.

a)

A

b)

B

c)

C

d)

D

52.

a)

A

b)

B

c)

C

d)

D

53.

a)

A

b)

B

c)

C

d)

D

54.

a)

A

b)

B

c)

C

d)

D

55.

a)

A

b)

B

c)

C

d)

D

56.

a)

A

b)

B

c)

C

d)

D

57.

a)

A

b)

B

c)

C

d)

D

58.

a)

A

b)

B

c)

C

d)

D

59.

What is the first step when factoring polynomials?

a)

Find the GCF

b)

List all the terms

c)

Make the X and fill in the top and bottom

d)

Multiply a and c

60.

Factor using GCF or monomial factoring:

2n²-8n³

a)

2n²(n-4n²)

b)

2n²(1-4n)

c)

2n³(10-8n²)

d)

3n(1-4n)

61.

What is the common monomial factor of $6x^3+3x^2-12x$ ?

a)

$3$

b)

$2x$

c)

$3x$

d)

$3x^2$

62.

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

a)

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

b)

$\left(8+x^2y\right)\left(8-x^2y\right)$

c)

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

d)

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

63.

The factored form of m²+ 6m + 5 is

(m+2)(m+ 3)

a)

true

b)

false

64.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

65.

A rectangle has an area of 4x²+19x + 12 and a length of (x + 4). What is the width?

a)

4x - 3

b)

4x + 3

c)

2x + 6

d)

2x + 3

66.

Factor completely: x²+16x+64

a)

(x+4)(x+16)

b)

(x-8)(x-8)

c)

(x+2)(x+32)

d)

(x+8)(x+8)

67.

Factor completely: x²-13x+40

a)

(x-5)(x-8)

b)

(x+5)(x+8)

c)

(x-4)(x-10)

d)

(x-2)(x-20)

68.

Factor:
2x² + 13x + 15

a)

(2x + 1)(x + 15)

b)

(x + 3)(x + 5)

c)

(2x - 3)(x - 5)

d)

(2x + 3)(x + 5)

69.

Factor the polynomial

x^2-36

a)

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

b)

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

c)

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

d)

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

70.

Factor the polynomial

9x^2-1

a)

$\left(9x+1\right)\left(x-1\right)$

b)

$\left(3x+1\right)^2$

c)

$\left(3x-1\right)^2$

d)

$\left(3x+1\right)\left(3x-1\right)$

71.

Factor the polynomial

81-m^2

a)

$\left(9m+1\right)\left(9m-1\right)$

b)

$\left(9+m\right)\left(9-m\right)$

c)

$\left(9-m\right)^2$

d)

$\left(9m+1\right)^2$

72.

Factor the polynomial

1-25y^2

a)

$\left(5+y\right)\left(5-y\right)$

b)

$\left(1-5y\right)^2$

c)

$\left(1+5y\right)\left(1-5y\right)$

d)

$\left(1+5y\right)^2$

73.

Factor the polynomial

k^2+14k+49

a)

$\left(k+7\right)^2$

b)

$\left(k-7\right)^2$

c)

$\left(k+7\right)\left(k-7\right)$

d)

$\left(k+2\right)\left(k+7\right)$

74.

Factor the polynomial

m^2-18m+81

a)

$\left(m+9\right)^2$

b)

$\left(m-9\right)^2$

c)

$\left(m+9\right)\left(m-9\right)$

d)

$\left(m-1\right)\left(m-18\right)$

75.

Solve the equation

w^2-25=0

a)

$w=25$ and $w=-25$

b)

$w=5$ and $w=-5$

c)

$w=5$

d)

$w=25$

76.

Solve the equation

p^2+8p+16=0

a)

$p=4$ and $p=-4$

b)

None of these

c)

$p=4$

d)

$p=-4$

77.

Solve the equation

x^2-22x+121=0

a)

$x=11$ and $x=-11$

b)

None of these

c)

$x=11$

d)

$x=-11$

78.

Solve the equation

x^2-36=0

a)

$x=6$ and $x=-6$

b)

$x=6$

c)

$x=-6$

d)

None of these

Factoring Trinomials ax^2

Total questions: 78

Worksheet time: 8hrs 43mins

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