Solving Polynomials in Factored Form

You can take this as many times as you'd like!

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​2.4-2.8 REVIEW for Factoring QUIZ

​2.4: Solving in Factored Form

2.5 ​: Factoring x² + bx + c

2.6 ​: Factoring ax² + bx + c​

2.7: Factoring Special Products (Difference of 2 Squares & Perfect Square Trinomials)

2.8: Factoring/Solving Polynomials Completely​

• ​Set each factor equal to zero.

• ​Solve all "mini" equations.

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2.4

Solving in Factored Form

Multiple Choice

Solve the equation

$$x\left(x-5\right)=0$$  

• $$x=0$$  

• $$x=5$$  

• $$x=0$$  and  $$x=5$$  

• No solution

Multiple Choice

Solve the equation

$$6d\left(d+8\right)=0$$  

• $$d=0$$  and  $$d=-8$$  

• $$d=6$$  and  $$d=-8$$  

• $$d=0$$  and  $$d=8$$  

• $$d=6$$  and  $$d=8$$  

Multiple Choice

Solve the equation

$$\left(x-3\right)\left(x+5\right)=0$$  

• $$x=-3$$  and  $$x=5$$  

• $$x=3$$  and $$x=-5$$  

• $$x=3$$  

• $$x=-15$$  

Multiple Choice

Solve the equation

$$\left(3x+6\right)\left(2x-10\right)=0$$  

• $$x=-2$$  and  $$x=5$$  

• $$x=2$$  and $$x=-5$$  

• $$x=-6$$  and  $$x=10$$  

• $$x=6$$  and $$x=-10$$  

Multiple Choice

Solve the equation

$$\left(y-10\right)^2=0$$  

• $$x=-10$$  and  $$x=5$$  

• $$x=10$$  

• $$x=-10$$  

• $$x=10$$  and  $$x=-10$$  

• ​Find factors that multiply to "c" and add to "b".

• ​Place each factor in its own binomial with x.

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2.5

Factoring x² + bx + c

Multiple Choice

Factor
x² + 9x - 36

• (x + 12)(x - 3)
• (x + 9)(x - 4)
• (x - 12)(x + 3)
• (x - 9)(x - 4)

Multiple Choice

Factor
n² + 16n + 63

• (n-7)(n+4)
• (n+7)(n-9)
• (n-3)(n-10)
• (n+7)(n+9)

Multiple Choice

Factor
x² - 5x - 36

• (x - 4)(x + 9)
• (x - 6)(x + 6)
• (x + 4)(x - 9)
• (x -12)(x + 3)

Multiple Choice

Factor
k² - 2k - 24

• (k+4)(k-6)
• (k+4)(k+6)
• (k+6)(k-1)
• (k-4)(k+6)

Multiple Choice

Factor.

$$v^2+11v+28$$  

• $$\left(v-7\right)\left(v+4\right)$$  

• $$\left(v+7\right)\left(v-4\right)$$  

• $$\left(v+6\right)\left(v+3\right)$$  

• $$\left(v+7\right)\left(v+4\right)$$  

• ​Find factors that multiply to "ac" and add to "b".

• ​Rewrite middle term with chosen factors.

• Factor ​using preferred method:

  • Grouping

  • Divide by a

    • AKA "Bottoms Up"

  • Cross Factors

    • AKA Cross Multiply

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2.6

Factoring ax² + bx + c

Multiple Choice

Factor : 3x² - 7x - 6

• (3x + 2)(x - 3)
• (3x - 2)(x + 3)
• (3x - 3)(x + 3)
• (3x - 4)(x - 2)

Multiple Choice

Factor
3v² - 4v - 7

• (3v-7)(v+1)
• 3(v-7)(v-1)
• (3v+1)(v-9)
• (3v+1)(v-10)

Multiple Choice

Factor:
 2m² + 3m - 9

• 2(m + 3)(m - 3)
• (2m - 3)²
• (m + 3)(2m - 3)
• (2m + 3)(m - 3)

Multiple Choice

Factor
5x²-28x+32

• (3x-10)(x+6)
• (x-8)(5x-4)
• (5x-8)(x-4)
• (5x-8)(x+7)

Multiple Choice

Solve by factoring: x² - 9x + 20 = 0

• x = -4 and x = -5
• x = 20 and x = -9
• x = 4 and x = 5
• x = -4 and x = 5

• ​Is it a binomial?

• ​Is it subtraction?

• Are BOTH terms perfect squares?​

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2.7

Factoring Special Products

• ​Is it a trinomial?

• ​Are the FIRST and LAST terms perfect squares?

• Is the middle term equal to double the product of each square root?​

• ​Check if it fits the pattern for Difference of Two Squares OR Perfect Square Trinomial.

• If it does, follow the pattern and you're done!​

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Match

Match the following:

• Perfect Square Trinomial

• Difference of 2 Squares

• Prime (unfactorable)

4x²-32x+64

x²-1

x²+1

• 4x²-32x+64

• x²-1

• x²+1

Multiple Choice

x² - 25

• ( x + 5 ) ( x - 5 ) 
• ( x - 5 ) ( x - 5 ) 
• ( x + 5 ) ( x + 5 ) 
• Prime

Multiple Choice

x² - 16

• Prime
• ( x - 4) ( x + 4) 
• ( x - 8) ( x + 8) 
• ( x - 4) ( x - 4) 

Multiple Choice

Factor

x² + 18x + 81

• (x + 9)(x – 9)

• (x + 18)²

• (x + 9)²

• (x + 6)²

Multiple Choice

Factor: x² - 30x + 225

• (x + 15)²
• (x - 15)²
• (x + 25)²
• (x - 25)²

2.8

Factoring Completely

• ​Factor out GCF if possible.

• Look for special products.

• Factor.

• Solve if set equal to 0​.

  • "Mini" equations of each factor equal to 0.​

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Multiple Choice

Factor completely:

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

• 3(x² + 6x + 5)
• (x + 5)(x + 1)
• 3(x + 5)(x + 1)
• Prime

Multiple Choice

Factor Completely $$6p^2+90p+300$$  

• $$6\left(p+5\right)\left(p+10\right)$$  

• $$5\left(p-6\right)\left(p-10\right)$$  

• $$6\left(p+5\right)\left(p-10\right)$$  

• $$\left(p+8\right)\left(p+9\right)$$  

Multiple Choice

Factor Completely $$5x^2+20x-105$$  

• $$5\left(x-3\right)\left(x+7\right)$$  

• $$5\left(x+3\right)\left(x-7\right)$$  

• $$5\left(x-3\right)\left(x-7\right)$$  

• Not Factorable 

Multiple Choice

Solve for y.
2y² + 3y - 2 = 0 

• y = -2 or y = 1/2
• y = -1 or y = 2
• y = -2 or y = 1
• y = -1/2 or y = 2

Multiple Choice

Solve the equation. 6x² + x = 15

• x = -2/3 or x = 1

• x = -5/3 or x = -3/2

• x = 3/5 or x = -2

• x = -3/2 or x = 5

Multiple Select

 Factor and solve for p $$3p^3+9p^2-210p=0$$

• p = 0

• p = -10

• p = 7

• p = 10

• p = -7