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### Middle/High School Algebra, Geometry, and Statistics (AGS)4.3 Factorization of any Quadratic Polynomial - I

 Method of Factorization: 1. Multiply the coefficient of x2 by the constant term. 2. Resolve this product into two factors such that their sum is the coefficient of x. 3. Rewrite the x term as the term of two terms with these coefficients. 4. Then we can find the factors. Example: Factorize, 6x2+19x+15. Solution: Given that, 6x2+19x+15. Here x2 coefficient is 6 and constant term is 15, the product of these terms is = 6 * 15 = 90 19 = 10 + 9 = 10 * 9 = 90. Therefore, 6x2+19x+15 = (6x2+10x)+(9x+15). Take 2x and 3 as common, we get = 2x(3x+5)+3(3x+5) Take (3x+5) as common, we get = (3x+5)(2x+3) Directions: Solve the following problems. Also write at least ten examples of your own.
 Q 1: Factorize, x2+11x+30.(2x+5)(x+3)(2x+5)(x+6)(3x+2)(x+7)(x+5)(x+6) Q 2: Factorize, 2x2+17x+30.(2x+3)(2x+1)(2x+5)(x+6)(8x+2)(x+5)(3x+2)(x+7) Q 3: Factorize, 6x2+25x+21.(8x+2)(x+5)(2x+3)(2x+1)(6x+7)(x+3)(2x+5)(x+6) Q 4: Factorize, 4x2+8x+3.(2x+3)(2x+1)(3x+2)(x+7)(8x+2)(x+5)(2x+5)(x+6) Q 5: Factorize, 3x2+23x+14.(2x+5)(x+3)(3x+2)(x+7)(8x+2)(x+5)(7x+5)(x+3) Q 6: Factorize, 7x2+26x+15.(7x+5)(x+3)(2x+5)(x+3)(3x+2)(x+7)(2x+5)(x+6) Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!