Review: Factoring by GCF 1. Find the GCF for 30x3 + 5x2 - 25x ; then simplify A: Factor the coefficients. What is the GCF for 30, 5, & 25? B: Divide each term by the GCF to complete the problem.**Note: Most simplifying can be done through mental math.What you are doing is dividing a monomial by a monomial. 30x3 + 5x2 - 25x = 5x(6x2 + x - 5) 5x 5x 5x
Special Case Binomials : Square of Sums: 1. (x + 1) 2 2. (3x + 1)2All +, + perfect square trinomials factor into square ofsum binomials.The product of a Square of a Sum binomial (a + b)2 is: a2 + 2ab + b2
Special Case Binomials : Square of a Difference: 1. (x - 4) 2 2. (3x - 1)2All -, + perfect square trinomials factor into square ofdifference binomials. The product of a Square of a difference binomial (a - b)2 is: a2 - 2ab + b2
DifferenceCase Two Squares Special of Binomials : Product of a Sum and a Difference:Another shortcut for factoring a trinomial is whenwe want to factor the difference of two squares. 1. (6x - 5)(6x + 5) a2 – b2 = (a + b)(a – b) 2. (m - 10)(m + 10) A binomial is the difference of two squares if: The product of a Sum and a difference is: 1.Both terms are squares and a2 - b2 2.The signs of the terms are of squares which is: The difference different. 9x2 – 25y2 or: of difference of squares:(a2 - b2) The factored form 4 a 4 –c +d is: The product of a sum and a difference
Warm Up:2. Find the length & width: 1st, 3rd, 4th Periods 2nd p.