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Perfect Square Trinomials
Form for Perfect Square Trinomials: a 2 + 2ab + b 2 OR a 2 – 2ab + b 2
When factoring: If the first term and last term are Perfect Squares, check for a perfect square Trinomial
When factoring: If the first term and last term are Perfect Squares, check for a perfect square Trinomial a 2 + 2ab + b 2 = (a + b) 2 Or a 2 – 2ab + b 2 = (a – b) 2
Example 1: x 2 + 6x + 9
Example 2: x 2 + 16x + 64
Practice 1: x 2 + 20x + 100
Factoring Trinomials with a Leading Coefficient
ax 2 + bx + c If a ≠ 1, then: 1.Create a list of factors for a and c
ax 2 + bx + c If a ≠ 1, then: 1.Create a list of factors for a and c 2.Find a combination of the factors of a and c that add up to b
ax 2 + bx + c If a ≠ 1, then: 1.Create a list of factors for a and c 2.Find a combination of the factors of a and c that add up to b 3.Write the binomials
Example 1: 3x 2 + 11x + 6
Example 2: 8x 2 – 10x – 3
Example 3: 16x 2 – 16x + 4
Practice 1: 5x 2 + 12x + 7
Practice 2: 6x 2 – 29x – 5
Practice 3: 12x 2 + 25x + 13
Warm-Up Factor the following expressions by pulling out things that each term has in common: 4x3 + 8x2 + 12xz 9x2y3 + 3xy2 + 27xy4.
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How do I solve quadratic equations? Notes Over Solving Quadratics Methods of Solving Quadratics Square Root Method: No bx term.
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Solving Quadratic Equations Using Square Roots & Completing the Square
Solving Quadratic Equations by Completing the Square
Quadratics – Completing the Square A Perfect Square Trinomial is any trinomial that is the result of squaring a binomial. Example 1: Binomial Squared Perfect.
4.7 – Complete the Square In lesson 4.5, you solved equations of the form x2 = k by finding the square roots. This method also works if one side of an.
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Factoring Polynomials. 1.Check for GCF 2.Find the GCF of all terms 3.Divide each term by GCF 4.The GCF out front 5.Remainder in parentheses Greatest Common.
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Lesson 5-11 Using Several Methods of Factoring
Factoring Checklist Works every time!. 1. Check to see if there is a GCF. If so, factor it out. 3xy² + 12xy.
Multiplication: Special Cases Chapter 4.5. Sum x Difference = Difference of Two Squares (a + b)(a – b) = (a – b)(a + b) =a 2 – b 2.
Solving Quadratic Equations. Review of Solving Quadratic Equations ax 2 +bx +c = 0 When the equation is equal to zero, solve by factoring if you can.
4.6 Completing the Square Completing a perfect square trinomial allows you to factor the completed trinomial as the square of a binomial. You can solve.
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