MATH Basic Algebra I  - Unit 17: Factoring

Prime Factorization


1)

Define factors. 


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2)

Define a multiple and give an example. 


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3)

Explain what common factors are and give an example. 


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4)

Define a prime number. 


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5)

Explain what composite numbers are. 


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For the following problems, factor each number into prime factors. (Hint: Use a factor tree.)


6)

900 


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7)

96


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8)

54


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Monomial Factors


9)

Factor the polynomial.


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10)

Factor the polynomial.


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11)

Factor the polynomial.


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12)

Factor the polynomial.


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13)

Factor the polynomial.


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14)

Factor by grouping.


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15)

Factor by grouping.

Hint:  You may need to factor out a negative number.


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Factoring Trinomials


16)

Factor the trinomial.


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17)

Factor the trinomial.


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18)

Factor the trinomial.


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19)

Factor the trinomial.


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20)

Explain how the signs of the trinomial affect the signs of the factors. 


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Factoring Trinomials in the form of ax2 + bx + c (a > 1)


21)

Explain the factoring process of trial and error. 


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22)

Factor using trial and error.


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23)

Factor using trial and error.

Hint:  These factors will have different signs for the constant term.


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24)

Factor using trial and error.


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25)

Factor using trial and error.


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26)

Factor using difference of squares.


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Solving Quadratic Equations


27)

What property is used in solving quadratic equations? 


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28)

What are the zeros of a quadratic equation?


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29)

Solve the equation by factoring.

Hint:  Factor first, then set each factor equal to zero and solve each equation separately for the two answers


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30)

Solve the equation by factoring.


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31)

Solve the equation by factoring.


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32)

Solve the equation by factoring.


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Review


33)

Solve the equation for “x.


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34)

Solve the equation for “z.


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