Give the Missing Factor Factor and Solve Equations Factor a Trinomial Mixed Factoring 10 10 10 10 20 20 20 20 30 30 30 30 40 40 40 40 50 50 50 50 Click here for game DIRECTIONS Hardtke Jeopardy Template 2011

X2 – 121  (x – 11)( ? ) Click to check answer 10 Give the Missing Factor X2 – 121  (x – 11)( ? ) Click to check answer X + 11 This is a Difference of Squares and thus it factors into two conjugates. Click to return to game board

x2 – 18x2 + 81  (x – 9) ( ? ) Click to check answer 20 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 Click to return to game board

6x3 – 39x2 – 21x 3x(x – 7) ( ? ) Click to check answer 30 Give the Missing Factor 6x3 – 39x2 – 21x 3x(x – 7) ( ? ) Click to check answer (2x + 1) Step 1: 3x(2x2 – 13x – 7) Step 2 is to reverse FOIL Click to return to game board

x3 – 27y3  (x – 3y) ( ? ) Click to check answer 40 Give the Missing Factor x3 – 27y3  (x – 3y) ( ? ) Click to check answer (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) ( ? ) Click to check answer 50 Give the Missing Factor x4 – 7x2 + 10  (x2 – 5) ( ? ) Click to check answer x2 – 2 Notice this is a “quartic” (4th degree) that factors just like a “quadratic” trinomial (2nd degree) Click to return to game board

x2 – 49 = 0 Click to check answer 10 Factor and Solve the Equation x2 – 49 = 0 Click to check answer { – 7, 7} Step 1 – DOTS: (x – 7)(x + 7) = 0 Click to return to game board

6x2 + x – 1 = 0 Click to check answer 20 Factor and Solve the Equation 6x2 + x – 1 = 0 Click to check answer − 𝟏 𝟐 , 𝟏 𝟑 Step 1 – FOIL: (3x – 1)(2x + 1) = 0 Step 2 – Set each factor to zero: 3x – 1= 0 2x + 1 = 0 3x = 1 2x = – 1 Click to return to game board

10x3– 65x2 + 75x= 0 Click to check answer 30 Factor and Solve the Equation 10x3– 65x2 + 75x= 0 Click to check answer 0, 3 2 , 5 Step 1 – GCF: 5x(2x2 – 13x + 15) = 0 Step 2 – Foil: 5x(2x – 3)(x – 5) = 0 Click to return to game board

x4– 10x2 + 9 = 0 Click to check answer 40 Factor and Solve the Equation x4– 10x2 + 9 = 0 Click to check answer { – 3, – 1, 1, 3} Step 1 – FOIL: (x2 – 1)(x2 – 9) = 0 Step 2 – DOTS: (x – 1)(x + 1)(x – 3)(x + 3) = 0 Click to return to game board

x2(x – 5) – 9(x – 5) = 0 Click to check answer 50 Factor and Solve the Equation x2(x – 5) – 9(x – 5) = 0 Click to check answer { – 3, 3, 5} Step 1 – GCF: (x – 5)(x2 – 9) = 0 Step 2 – DOTS: (x – 5)(x – 3)(x + 3) = 0 Click to return to game board

4x2 + 20x + 25 Click to check answer 10 Factor a Trinomial 4x2 + 20x + 25 Click 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. Click to return to game board

4ax2 – 44ax – 48a Click to check answer 20 Factor a Trinomial 4ax2 – 44ax – 48a Click to check answer 4a(x – 12)(x + 1) Step 1 – GCF: 4a(x2 – 11x – 12) Step 2 – FOIL: 4a( x – 12)(x + 1) Click to return to game board

18x2 + 21x – 30 Click to check answer 30 Factor a Trinomial 18x2 + 21x – 30 Click to check answer 3(6x – 5)(x + 2) Step 1 – GCF: 3(6x2 + 7x – 10) Step 2 – FOIL: 3(6x – 5)(x + 2) Click to return to game board

x2(a+3) − x(a+3) − 30(a+3) Click to check answer 40 Factor a Trinomial x2(a+3) − x(a+3) − 30(a+3) Click to check answer (a+3)(x – 6)(x + 5) Step 1 – GCF: (a+3)(x2 – x – 30) Step 2 – FOIL: (a+3)( x – 6)(x + 5) Click to return to game board

(y+2)x3– 13(y+2)x2 + x(y+2) Click to check answer 50 Factor a Trinomial (y+2)x3– 13(y+2)x2 + 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. Click to return to game board

x2(a – b) – 9(a – b) Click to check answer 10 Mixed Factoring x2(a – b) – 9(a – b) Click to check answer (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

12x3 – 27xy2 Click to check answer 20 Mixed Factoring 12x3 – 27xy2 Click to check answer 3x(2x – 3y)(2x + 3y) Step 1 – GCF: 3x(4x2 – 9y2) Step 2 is DOTS Click to return to game board

wx3 – 64wy3 Click to check answer 30 Mixed Factoring wx3 – 64wy3 Click to check answer 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

5acx – 15ac – 5bcx + 15bc Click to check answer 40 Mixed Factoring 5acx – 15ac – 5bcx + 15bc Click 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] Click to return to game board

7x2 – 42x + 63 – 28y10 Click to check answer 50 Mixed Factoring 7x2 – 42x + 63 – 28y10 Click to check answer 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

Return to main game board 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. Return to main game board