#4 Factor each polynomial completely. If a polynomial cannot be factored, write prime. a) t +...
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#4 Factor each polynomial completely. If a polynomial cannot be factored, write "prime". a) t² + 4t-12 b) a²-a-12 List possible combinations: List possible combinations: Factored form: c) x² - 7x+12 List possible combinations: Factored form: (3) Special products: Difference of squares: in the form ()²-()² a²b² = (a + b)(a - b) Perfect square trinomials: First term and last terms are perfect squares and the middle term is twice the product of first and last terms > a² + 2ab + b² = (a + b)² a²-2ab + b² = (a - b)² #5 Factor the following: a) x² - 36 c) r²-8r+16 Factored form: d) x² + 13x + 12 List possible combinations: Factored from: a) 4x² - 49 = (2x)²-7² = (2x + 7)(2x-7) x² + 6x +9 b) c) = (x)² + 2(3)(x) +3² = (x+3)² 4x² - 20x + 25 = (2x)²-2(2x)(5) +5² = (2x - 5)² b) p² + 10p +25 d) 49-² 2 #6 Factor each polynomial completely. If a polynomial cannot be factored, write "prime". a. 2x² - 6x-8 GCF = b. 3y² + 2y-1 GCF= c. 2x² - 7x+5 (3) Solving quadratic equations by factoring Zero-factor property: Ifa.b=0⇒a=0 or b=0 GCF= ➤ One side is in factored form The other side is 0 #7 Solve each equation. a) x² - 8x = 0 c) 9-4x² = 0 d. 3w²-2w-21 GCF= Example: Solve x² + 3x = 4 x² + 3x -4 = 0 Make one side 0 (x+4)(x-1)= 0 Factor the other side ⇒x+4= 0 orx-1=0 Set each factor to 0 ⇒x=-4 or x = 1 Solve each equation for x b) x² - 8x = 9 d) 2x² + 3x + 1 = 0 #4 Factor each polynomial completely. If a polynomial cannot be factored, write "prime". a) t² + 4t-12 b) a²-a-12 List possible combinations: List possible combinations: Factored form: c) x² - 7x+12 List possible combinations: Factored form: (3) Special products: Difference of squares: in the form ()²-()² a²b² = (a + b)(a - b) Perfect square trinomials: First term and last terms are perfect squares and the middle term is twice the product of first and last terms > a² + 2ab + b² = (a + b)² a²-2ab + b² = (a - b)² #5 Factor the following: a) x² - 36 c) r²-8r+16 Factored form: d) x² + 13x + 12 List possible combinations: Factored from: a) 4x² - 49 = (2x)²-7² = (2x + 7)(2x-7) x² + 6x +9 b) c) = (x)² + 2(3)(x) +3² = (x+3)² 4x² - 20x + 25 = (2x)²-2(2x)(5) +5² = (2x - 5)² b) p² + 10p +25 d) 49-² 2 #6 Factor each polynomial completely. If a polynomial cannot be factored, write "prime". a. 2x² - 6x-8 GCF = b. 3y² + 2y-1 GCF= c. 2x² - 7x+5 (3) Solving quadratic equations by factoring Zero-factor property: Ifa.b=0⇒a=0 or b=0 GCF= ➤ One side is in factored form The other side is 0 #7 Solve each equation. a) x² - 8x = 0 c) 9-4x² = 0 d. 3w²-2w-21 GCF= Example: Solve x² + 3x = 4 x² + 3x -4 = 0 Make one side 0 (x+4)(x-1)= 0 Factor the other side ⇒x+4= 0 orx-1=0 Set each factor to 0 ⇒x=-4 or x = 1 Solve each equation for x b) x² - 8x = 9 d) 2x² + 3x + 1 = 0
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4 a t 2 4t 12 List of possible combinations 1 12 2 6 3 4 4 3 6 2 12 1 Factor form t 2t 6 b a 2 a 12 List of possible combinations 1 12 2 6 3 4 4 3 6 2 12 1 Factor form a 4a 3 c x 2 7x 12 List of possi... View the full answer
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Discovering Advanced Algebra An Investigative Approach
ISBN: 978-1559539845
1st edition
Authors: Jerald Murdock, Ellen Kamischke, Eric Kamischke
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