give t he missing factor

Givethe Missing

Factor

Factorand SolveEquations

Factora

TrinomialMixed

Factoring

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Hardtke Jeopardy Template 2011Click here for game DIRECTIONS

X2 – 121 (x – 11)( ? )Click to check answer

X + 11This is a Difference of Squares andthus it factors into two conjugates.

Click to return to game board

10 Give the Missing Factor

x2 – 18x2 + 81 (x – 9) ( ? )

Click to check answer

(x – 9)This is a PST, so it factors as (x – 9)2



6x3 – 39x2 – 21x3x(x – 7) ( ? )


(2x + 1)Step 1: 3x(2x2 – 13x – 7)Step 2 is to reverse FOIL



x3 – 27y3 (x – 3y) ( ? )


(x2 + 3xy + 9y2)The middle term is the opposite of the product of

the cube roots found in the binomial factor.Click to return to game board


x4 – 7x2 + 10 (x2 – 5) ( ? )


x2 – 2Notice this is a “quartic” (4th degree) that factors just

like a “quadratic” trinomial (2nd degree)



x2 – 49 = 0Click to check answer

{ – 7, 7}Step 1 – DOTS: (x – 7)(x + 7) = 0


10 Factor and Solve the Equation


Step 1 – FOIL: (3x – 1)(2x + 1) = 0Step 2 – Set each factor to zero: 3x – 1= 0 2x + 1 = 0 3x = 1 2x = – 1




Step 1 – GCF: 5x(2x2 – 13x + 15) = 0Step 2 – Foil: 5x(2x – 3)(x – 5) = 0




{ – 3, – 1, 1, 3}Step 1 – FOIL: (x2 – 1)(x2 – 9) = 0

Step 2 – DOTS: (x – 1)(x + 1)(x – 3)(x + 3) = 0Click to return to game board


x2(x – 5) – 9(x – 5) = 0Click to check answer

{ – 3, 3, 5}Step 1 – GCF: (x – 5)(x2 – 9) = 0

Step 2 – DOTS: (x – 5)(x – 3)(x + 3) = 0



4x2 + 20x + 25Click to check answer

(2x +5)(2x + 5) or (2x + 5)2

This is a PST. When the 1st & 3rd terms are squares always check first to see if a binomial squared

will give the correct middle term.


10 Factor a Trinomial


4a(x – 12)(x + 1) Step 1 – GCF: 4a(x2 – 11x – 12)Step 2 – FOIL: 4a( x – 12)(x + 1)




3(6x – 5)(x + 2) Step 1 – GCF: 3(6x2 + 7x – 10)Step 2 – FOIL: 3(6x – 5)(x + 2)




(a+3)(x – 6)(x + 5) Step 1 – GCF: (a+3)(x2 – x – 30)Step 2 – FOIL: (a+3)( x – 6)(x + 5)



x(y+2)Click to check answer

x(y+2)(x2 – 13x + 1) Step 1: x(y + 2) is a GCF of all three terms

Then the leftover trinomial is prime,so you’re done.



x2(a – b) – 9(a – b)


(a – b)(x – 3)(x + 3)Step 1 (a – b) is the GCF: (a – b)[x2 – 9]

Step 2 DOTS: (a – b)(x – 3)(x + 3)Click to return to game board

10 Mixed Factoring

12x3 – 27xy2Click to check answer

3x(2x – 3y)(2x + 3y)Step 1 – GCF: 3x(4x2 – 9y2)

Step 2 is DOTSClick to return to game board

20 Mixed Factoring

wx3 – 64wy3


w(x – 4y)(x2 + 4xy + 16y2)Step 1 – GCF: (w)[x3 – 64y3]

Step 2 – Diff of Cubes: w(x – 4y)(x2 + 4xy + 16y2)Click to return to game board

30 Mixed Factoring

5acx – 15ac – 5bcx + 15bcClick to check answer

5c(a – b)(x – 3)Step 1 – GCF of all terms: 5c(ax – 3a – bx + 3b)

Step 2 – Grouping: 5c[a(x – 3) – b(x – 3)]Step 3 – GCF: 5c(x – 3)[a– b]


40 Mixed Factoring

7x2 – 42x + 63 – 28y10


7(x – 2y5 – 3)(x + 2y5 – 3)Step 1 – GCF of all terms: 7( x2 – 6x + 9 – 4y10)

Step 2 – Grouping 3 X 1: 7[ (x – 3)2 – 4y10]Step 3 – DOTS:

7[ (x – 3) – 2y5] [ (x – 3) + 2y5]Click to return to game board

50 Mixed Factoring

Jeopardy Directions• Any group member may select the first question and students rotate choosing the next

question in clockwise order regardless of points scored.

• As a question is exposed, EACH student in the group MUST write his solution on paper. (No verbal responses accepted.)

• The first student to finish sets down his pencil and announces 15 seconds for all others to finish working.

• After the 15 seconds has elapsed, click to check the answer.– IF the first student to finish has the correct answer, he earns the point value of the question and no

other students earn points.– IF that student has the wrong answer, he subtracts the point value from his score and EACH of the

other students with the correct answer earns/steals the point value of the question. (Those students do NOT lose points if incorrect, only the first student to “ring in” can lose points in this game version.)

• Each student should record a running total of his own score.

• Good sportsmanship and friendly assistance in explaining solutions is expected! Reviewing your math concepts is more important than winning.

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give t he missing factor

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