pick any 3 methods of factoring - give 3 examples for each method and show the complete solution​

Here are three common methods of factoring, with three examples for each.1. Factoring out the Greatest Common Factor (GCF)This method involves finding the largest term that can divide into all terms of the polynomial.Example 1: 3x^2 + 6x * The GCF of 3x^2 and 6x is 3x. * 3x^2 \div 3x = x * 6x \div 3x = 2 * Solution: 3x(x + 2)Example 2: 12a^3b^2 - 18a^2b^3 + 6ab * The GCF is the product of the GCF of the coefficients (6) and the lowest power of each variable (a and b). The GCF is 6ab. * 12a^3b^2 \div 6ab = 2a^2b * -18a^2b^3 \div 6ab = -3ab^2 * 6ab \div 6ab = 1 * Solution: 6ab(2a^2b - 3ab^2 + 1)Example 3: 5y^4 - 10y^3 + 25y^2 * The GCF is 5y^2. * 5y^4 \div 5y^2 = y^2 * -10y^3 \div 5y^2 = -2y * 25y^2 \div 5y^2 = 5 * Solution: 5y^2(y^2 - 2y + 5)2. Factoring a Difference of Two SquaresThis method applies to binomials in the form a^2 - b^2. It factors into (a - b)(a + b). Both terms must be perfect squares and separated by a minus sign.Example 1: x^2 - 9 * x^2 is a perfect square (x \cdot x) * 9 is a perfect square (3 \cdot 3) * Solution: (x - 3)(x + 3)Example 2: 16m^4 - 25n^2 * 16m^4 is a perfect square ((4m^2) \cdot (4m^2)) * 25n^2 is a perfect square ((5n) \cdot (5n)) * Solution: (4m^2 - 5n)(4m^2 + 5n)Example 3: 49y^6 - 1 * 49y^6 is a perfect square ((7y^3) \cdot (7y^3)) * 1 is a perfect square (1 \cdot 1) * Solution: (7y^3 - 1)(7y^3 + 1)3. Factoring Trinomials (ax^2 + bx + c)For simple trinomials where a=1, you find two numbers that multiply to c and add up to b.Example 1: x^2 + 5x + 6 * Find two numbers that multiply to 6 and add to 5. * The numbers are 2 and 3. (2 \cdot 3 = 6 and 2 + 3 = 5) * Solution: (x + 2)(x + 3)Example 2: x^2 - 8x + 15 * Find two numbers that multiply to 15 and add to -8. * The numbers are -3 and -5. (-3 \cdot -5 = 15 and -3 + (-5) = -8) * Solution: (x - 3)(x - 5)Example 3: x^2 + 2x - 8 * Find two numbers that multiply to -8 and add to 2. * The numbers are 4 and -2. (4 \cdot -2 = -8 and 4 + (-2) = 2) * Solution: (x + 4)(x - 2)

Answered by armamentomelanie | 2025-08-23