TenMarks teaches you how to solve quadratic equations using factoring.
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Factoring So in the problem, we need to sub each quadratic equation by factoring and check our answer. Before we begin, to factor a trinomial equation of the form, the form is AX²+BX+C=0. So to factor this, we need to find two integer factors. So in order to factor, we need to find two integer factors. So, we need to find A and C, the factors of A and C that their sum such that their sum is equal to B. So, if the two factors of A and C are M and N, the factored equation then becomes AX²+MX+NX+C=0. So, when you're factoring a trinomial equation, you have to find the factors of A and C such that the factors of A and C, if you add them, they equal B and then the two factors then become M and N. So then, the factored equation would be AX²+MX+NX+C, so your two factors become part of your factored equation. So, let’s go ahead and move to our first problem in A and sub this one. So, we need to sub it by factoring. So, X²+14X+49=0 this is a trinomial equation. So, we need to factor the equation before using the zero product property. So, the first step we need to do is we need to factor this trinomial equation. So to factor this equation, we need to find the factors of A and C, so we need to find the factors of 1 and 49, so basically 49. But the factors of 49 needs to equal the sum of 14 so I know that 7*7=49, so two factors of 7 or 49 are 7 and I know that 7+7=14 which gives me my B. So then, that means 7 and 7 are my factor that becomes M and N. So now, we can go ahead and put this in factored equations. So, X²+14X+49=0 so this becomes X² plus, now it’s MX so it’s 7X+MX which is 7X+49=0. So now, we need to go ahead and factor out our X and our 7. So if I factor out my Xs, I get X*X+7 plus and I factor out my 7 so I'm going to take 7*X+7=0 and now, I'm going to factor out my X+7 and so then I get X+7*X+7=0. My second step now is going to be to use the zero product property. So, I know that X+7=0 or X+7=0. Well now, my next step is going to be to sub. So, I'm going to go ahead and sub. Well, X+7=0 gives me X=-7 and then X+7=0 gives me X=-7. So X=-7, both factors result in the same solution X=-7. So now, I'm going to go ahead and check, so let me give myself a little more room here to check my answers. So my next step is to go ahead and check. So now, I'm going to go and substitute X for -7 in the original equation. So, my original equation is X²+14X+49. So, I'm going to go ahead and rewrite that X²+14X+49=0 and I'm going to go ahead and plug in -7 everywhere I see an X. So -7²+14*-7+49=0, -7² is 49-14*-7 is 98 so it becomes -98-98+49 and then that would be 98-98 because 49 and 49 is 98, 98-98 is 0. So, since both the size of the equation are -7 is the solution. So both sides of the equation are equal, -7 is our solution. Let’s go ahead and move to our second one here. So now, we need to write the equation in standard form. So, that means we need to subtract 15 from both sides. So, this is not written in standard form yet, so we have to go ahead and put it in standard form before we can do anything else. So to put it in standard form, I'm just going to subtract 15 from both sides and then I get X²+2X-15=0. Now, this equation is written in standard form and now we can move on to sub. Now we have a trinomial. So, we’re going to go ahead and factor it. So, our first step is to factor our trinomial. So, we need to find the integers whose factors of 15 if we add them equal to. So, we’re looking for -15, the factors in -15 who equal to. So, I know that -3*5 is equal to -15 and -3+5 would give me two. So now, I have my M and my N. So now, I'm going to go ahead and plug this in. So, X²+2X-15 is equal to X²+MX which should be -3X+NX which should be 5X=15. Remember, if we go back up here, we took our trinomial equation and our factors M and N and it becomes our factored equation. So, M and NX are two factors and that’s what we just plugged in right here. These were two factors and we just plugged them in. So now, go ahead and X²+2X-15=0 and X²-3