Factoring: A General Strategy 5.6 Choosing the Right Method

To Factor a Polynomial A. Always look for a common factor first. If there is one, factor out the largest common factor. Be sure to include it in your final answer. B. Then look at the number of terms. Two terms: If you have a difference of squares, factor accordingly: A2 – B2 = (A – B)(A + B). Three terms: If the trinomial is a perfect-square trinomial, factor accordingly: A2 + 2AB + B2 = (A + B)2 or A2 – 2AB + B2 = (A – B)2. If it is not a perfect- square trinomial, try using FOIL or grouping. Four terms: Try factoring by grouping.

To Factor a Polynomial (continued) C. Always factor completely. When a factor can itself be factored, be sure to factor it. Remember that some polynomials, like A2 + B2, are prime. D. Check.

Factor: 25t4  15,625. Solution

Factor: 2x3 + 14x2 + 3x + 21 Solution

Factor: x5  2x4 + 24x3 Solution

Factor: x2  18x + 81 Solution

Factor: 12x2y3 + 20x3y4 + 4x2y5 Solution

Factor: ab + ac + wb + wc Solution

Factor: 36x2 + 84xy + 49y2 Solution

Factor: a8  16b4 Solution