Quiz on Factoring:

Hint:

    Look for Factors first:

    Then common factor:

Quiz Practice:

1. 6x + 2
2. 5x² + x
3. 15y -20y⁴
4. -2x⁵ + 4x⁴
5. 13h² -13h
6. a⁴ – a³ + a²
7. 6s + 15s⁴ -21s⁸
8. 14z⁶ – 35z⁹ - 42z^{4  (divide}
9. 9p³ +27p⁵ -6p¹⁰ + 12p¹²
10. -20q⁸ -8q²⁰ – 40q¹² –80q¹⁰

Answer Key:

Factor each expression:

1. 6x + 2
   1. 6: 1, 2, 3, 6
   2. 2: 1, 2

Solution: (6x / 2 = 3x) (2 / 2 = 1)

Answer: 2(3x +1)  

1. 5x²+ x
   1. 5 is composite number (1, 5)
   2. x is the common factor

Answer: x(5x + 1)

1. 15y -20y⁴
   1. 15y: 1, 3, 5, and 15
   2. 1, 2, 4, 5, 10, and 20
   3. Y is the common factor and 5

Answer: 5y(3 – 4y³)

1. -2x⁵ + 4x⁴
   1. Factor of -2: -1, and -2
   2. Factor of  4: 1, 2, and 4
   3. Common factor: x⁴ is divisorable out of x⁵
   4. 2x⁴: -2x⁵ + 2x⁴ = -x = 2

Answer: 2x⁴(-x = 2)

1. 13h²-13h
   1. 1, 13 factor
   2. H is the common fact
   3. 1, 2 exponent and the lowest exponent is 1

Answer: 13h(h – 1) = 13h² -13h

1. a⁴ – a³ + a²
   1. a is the common factor
   2. the factor of exponent 4 is 1, 2, 4
   3. the factor of exponent 3 is 1, 3
   4. the factor of exponent 2 is 1, 2
   5. lowest exponent will be a²

Answer:  a² (a² – a + 1)

1. 6s + 15s⁴ -21s⁸
   1. 6: 1, 2, 3, and 6 9
   2. 15: 1, 3, 5, and 15
   3. 18: 1, 2, 3, 6 9, and 18
   4. S is common factor
   5. Exponent is 2

Answer: 3s(2 + 5s³ – 7s⁷)

1. 14z⁶ – 35z⁹ - 42z^{4  (divide}
   1. Factor 14: 1, 2, 7, and 14
   2. Factor 35: 1, 5, 7,  and 35
   3. Factor 42: 1, 2, 3, 6, 7, and  42
   4. Z is the common factor
   5. Lowest exponent is 4 (factor)

Answer: 7z⁴(2z² – 5z⁵ – 6) (14z⁶ – 35z⁹ – 42z⁴)

1. 9p³ +27p⁵ -6p¹⁰ + 12p¹²
   1. Factor 9: 1, 3, and 9 (multiplication)
   2. Factor of 27: 1, 3, 9
   3. Factor of 6: 1, 2, 3, and 6
   4. Factor of 12: 1, 2, 3, 4, 6, and 12
   5. 3 is the smallest exponent

Answer: 3p³ (3 + 9p² + 2p⁷ + 4p²)

1. -20q⁸ -8q²⁰ – 40q¹² –80q¹⁰
   1. Factor -20: 1, 2, 4, 5 10, and 20
   2. Factor 8: 1, 2, 4 and 8
   3. Factor 40: 1, 2, 4, 10, 20, 40
   4. Factor 80: 1, 2, 4, 8, 10, 20
   5. Smallest exponent is 8

Answer: -4q⁸(5q – 2q¹² – 10q⁴ – 20q²)