Square Root Method Trinomial Method when a = 1 GCF 1A.4 Factoring Square Root Method Trinomial Method when a = 1 GCF

Solving with Square Roots Get x2 or the binomial squared by itself Take the square root of BOTH sides of the equal sign Don’t forget the  sign Simplify

Solve by Taking Square Roots X = ± 2i

Solve by Taking Square Roots X = ± 3 2

Solve by Taking Square Roots X = ± 3

Solve by Taking Square Roots X = -4 ± 3 2

Solve by Taking Square Roots 5. 5(x – 4)2 = 125 X = -1 and 9

Solve by Taking Square Roots 6. - 3 5 x2 – 2 = -5 X = ± 5

Solve by Taking Square Roots 7. - 9x2 = 243 X = ± 3i 3

Solve by Factoring (a=1) Standard Form of a Quadratic Equation: ax2 + bx + c = 0 Put the equation in descending order from highest power to lowest power. List all the factors of c. Determine which factors of c when added together equal b. Create two binomials with the variable as the first term and set it equal to zero… (x )(x )= 0 Write in the factors that you determined from step 3. Set each binomial equal to zero and solve each one for your variable.

Solve by Factoring (a=1) 1. 8x + x2 + 7 = 0 x = -7 x = -1

Solve by Factoring (a=1) 4. x2 – x – 56 = 0 x = -7 x = 8

Solve by Factoring (a=1) 2. n2 – 11n + 10 = 0 n = 10 n = 1

Solve by Factoring (a=1) 3. m2 + m – 90 = 0 m = 9 m = -10

Solve by Factoring (a=1) 5. x2 – 5x – 104 = 0 x = -8 x = 13

Solve by Factoring When There is a Greatest Common Factor(GCF) Standard Form of a Quadratic Equation: ax2 + bx + c = 0 When a > 1, examine the factors of a, b and c to determine if there is a GCF (the largest number that a, b & c can all be divided by). Divide each term of the quadratic equation by the GCF. Put the GCF in front and the new trinomial from step 2 in parentheses, and set it equal to zero. Factor the trinomial like normal.

Solve by Factoring (GCF) 1. 2x2 + 6x – 108 = 0 x = -9 x = 6

Solve by Factoring (GCF) 2. 3x2 + 9x – 54 = 0 x = -6 x = 3