Factor each of the following

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Presentation transcript:

Factor each of the following 64x4 – 49y2 125x3 + 216 100x2 + 180x + 81 x2 - 18x + 80

Polynomial Arithmetic/ Factoring Quiz Simplify: (14x4 + 11x2 - 9x5) - (-14x + 5x5 - 12x2) Simplify: (4 + 2n3) + (5n3 + 2n2 - 9) Simplify: (6z2 - 5)(7z2 + 6z) Factor: 16x4 – 100y6 Factor: 16x4 – 18x3 + 12x6 Factor: 512x9 + 27x12 Factor: 2x2 + 7x – 9 Factor: 169x2 - 234x + 81

Polynomial Arithmetic/ Factoring Quiz Simplify: (14x4 + 11x2 - 9x5) - (-14x + 5x5 - 12x2) Simplify: (4 + 2n3) + (5n3 + 2n2 - 9) Simplify: (6z2 - 6z - 5)(7z2 + 6z2 - 5) Factor: 16x4 – 100y6 Factor: 16x4 – 18x3 + 12x6 Factor: 512x9 + 27x12 Factor: 2x2 + 7x – 9 Factor: 169x2 - 234x + 81

Solving for x in quadratics SWBAT solve for the value of x using factoring techniques and the zero product property SWBAT solve for the value of x using the quadratic formula

Solving by Factoring The standard form of quadratic equation is ax2 + bx + c = 0, where a ≠ 0. Once a quadratic is in standard form we can solve for x by factoring and applying the zero product property

Zero Product Property Zero Product Property If ab = 0, then a = 0 or b = 0 EXAMPLE: If (x + 3) (x – 7) = 0 then (x + 3) = 0 or (x – 7) = 0

Example 1. 16x2 = 8x

Example 2. x2 + 7x = 18

Example 3. 2x2 – 11x = -15

Practice Solve for x. 3x2 – 20x – 7 = 0 2x2 + 4x = 6 4x2 – 17x = 15

Factor each of the following then solve for x 4x2 – 14x + 6 = 0 3x2 + 28x = -9 2x2 – 9x - 13= 5

Objective SWBAT solve for the value of x using the quadratic formula

Factor each of the following then solve for x 2x2 – 7x + 6 = 0 4x2 + 12x = -9 x2 – 8x + 20 = 5

Quadratic formula sometimes the quadratic is too messy, or it doesn't factor at all, or you just don't feel like factoring. While factoring may not always be successful, the Quadratic Formula can always find the solution for X

Quadratic formula The Quadratic Formula uses the a, b, and c from ax2 + bx + c, to solve for the value of X The formula is:

Rules of the quadratic formula you MUST have your equation arranged in the form ax2 + bx + c = 0 DO NOT drop the square root or the plus/minus Remember order of operations under the square root The 2a in the denominator of the Formula is underneath everything

Steps Step 1: Identify a, b, and c Step 2: Plug in a, b, and c into the equation Step 3: Simplify the equation Step 4: SOLVE

Example Find the values of x that make x2 + 3x – 4 = 0

Example Find the values of x that make 2x2 – 4x = 3

Example Solve x(x – 2) = 4

Example Solve -4 + 9x2 + 12x = -4x2 + 6x

Practice 1) x2 – 5x + 3 = +3x 2) 4x2 + x – 6 = -2x2 3) 7x 2 + 3x = 2