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Many trinomials can be factored with integer solutions (roots). (what factor pair of 7 has a SUM of +8 ?) x2 + 8x + 7 = 0 (x + 7) (x - 1) (x + 7) (x + 1) (x - 7) (x - 1) (what factor pair of 5 has a SUM of +8 ?) Other trinomials CANNOT be factored with integer solutions (roots). x2 + 8x + 5 = 0 +5 and +1 -5 and -1 NONE Some trinomials like x2 + 8x + 5 = 0 do not factor smoothly (the answers are not integers). When this happens, use the QUADRATIC FORMULA: using a, b, c in the standard form of a quadratic equation: ax2 + bx + c = 0 The coefficient (the number in front) of x2 is "a" The coefficient (the number in front) of x is "b" QUADRATIC FORMULA: The constant (a number by itself) is "c" a x2 + x + = 0 b c a = 1 b = 8 c = 5 1 The coefficient (the number in front) of x2 is "a" The coefficient (the number in front) of x is "b" x2 + x + = 0 The constant (a number by itself) is "c" a x2 + x + = 0 8 b 5 c Plug these values into the quadratic formula Quadratic Formula: a = b = c = x2 + 15x + 26 = 0 Fill in the blanks: a = b = c = Plug the a,b, and c values into the quadratic formula: - 1 15 26 x2 + 15x + 26 = 0 ± Quadratic Formula: √ 2 ( ) * 2 - 4 * * Quadratic Formula: a = b = c = 4x2 - 15x + 2 = 0 Fill in the blanks a = b = c = Plug the a,b, and c values into the quadratic formula: - 4 -15 2 4x2 - 15x + 2 = 0 ± Quadratic Formula: √ 2 ( ) * 2 - 4 * * Quadratic Formula: a = b = c = x2 + 2 = 0 Fill in the blanks a = b = c = Plug the a,b, and c values into the quadratic formula: - 1 0 2 Quadratic Formula: ± x2 + 2 = 0 √ 2 ( ) * 2 - 4 * * Quadratic Formula: a = b = c = 7x2 - 2x = 0 Fill in the blanks a = b = c = Plug the a,b, and c values into the quadratic formula: - 7 -2 0 ± 7x2 - 2x = 0 Quadratic Formula: √ 2 ( ) * 2 - 4 * * a = 1 b = 8 c = 5 Drag and drop the three terms to the correct spots! 1 The (the number in front) of xis "b" The coefficient (the number in front) of x2 is "a" The (a number by itself) is "c" x2 + x + = 0 coefficient ? constant ? a x2 + x + = 0 8 b 5 c Plug these values into the formula quadratic ? |