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Lesson 5-3 Solve by Factoring - two terms

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What should you do when there are only 2 terms in the expression to be factored? 1. Look for a GCF 2. See if it is a DIFFERENCE OF SQUARES

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here we have two equations to solve by factoring binomials on the left meaning that we have two terms so in this one we have two terms and hopefully you will remember that I said that if we have two times we had two choices the first choice is to look for a GCF and the second choice is to look for a difference of squares it won't let me write there we go so we want to look for a GCF or a difference of squares when we have two terms so this first one on a we're going to look for a GCF and we're going to ask ourselves does any number divided evenly into both for and 169 and the answer is no and so they were going to ask ourselves okay can we split this into 2 Square factors so the 4x squared can be broken down into two x times 2x so that makes it a perfect square and 169 can be broken down into 13 time so we're going to factor that using the difference of squares pattern so it's going to be too at last 13 times 2x minus 13 equals 0 and then we're going to set each factor equal to zero to Salt so I'll set this Factor equal to zero and also saw that by subtracting 13 5 / 2 and then I'll do the same thing for this Factor so 2x minus 13 equals 0 and hopefully that you can see that you're just going to get the same number but with opposite signs from what you just had tattoo at equals 13 / 2 + x equals 13/2 Senior Solutions here are -13/2 and positive 13 hives for that can be Rewritten as + 4 - 13/2 so that's one example the other example also has two terms that 3x squared + -18 X so we going to look and see if these have a GCF and they do we can break down just in case you can easily see it we can break down 3 x squared into three times x times at and we can break down -18 into I will use them we'll just worry about the numbers right now three times six times at so I can see that they have three in common and because the first time doesn't have any other numbers we don't need to break down 6 more but they also both have X 3x is the greatest common factor what's left over from the first term is X bring down your minus sign what's left over from the second term is sick 3 x x x -6 is the factorization for that now we'll set each factor equal to zero and solve here so this is one of the factors and this is the other factor and sulfur reacts call Ciro did I like to meet me to ask equals 0 and then that's minus 6 equals 0 add  to both sides and you get at equal so your solution solution set is 0 + 6

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Lesson 5-3 Solve by Factoring - two terms

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