A Harvard University Entrance Exam question|solve for m| can you pass?

Hello everyone, let's solve this Harvard math question. Yes, so many people have failed it. Let's go. see why they failed this question now I want us to move this constant to this side before we Start factorization: so we have m cubed plus five m minus 42 equals zero. Okay, now 42 can be expressed as 27 plus 15, right? Yes, I chose 27 because 27 is a cube. is actually a cube, and so we can write m to the power of 3 plus 5m minus 27 plus 15. is equal to zero, excuse me, so we have m to the power of 3 plus 5m now minus times 27 We get minus 27 and minus times 15, we get minus 15, which is equal to zero. Now let's bring this cube to come and meet this, so we have m to the power of 3 minus 27 plus 5m minus 15 is equal to zero now 27 is the same thing as 3 to the power of 3, so we can write m to the power of }}, minus 3 to the power of 3 plus 5 m minus 15 is equal to zero. Now recall that when you have a cubed minus b cubed, which is equal to a minus b multiplied by a squared plus ab plus b squared, all right? Now, if we should relate this to this, our a is m and our b is 3, so that means we can express this as m minus 3 multiplied by m squared plus m multiplied by 3 plus 3 squared, right? That's it for this, then plus 5 brackets I want. to factorize this, and I'm factoring out 5 now; when 5m is divided by 5, we have m; minus when 15 is divided by 5, we have 3 is equal to zero, so we can write okay. Now when you look at this, you can See that we have m minus 3 here and we have m minus 3 here, but before that, let's simplify this. Furthermore, we are going to have (m minus 3) multiplied by (m squared plus 3m plus 9) plus 5. brackets m minus 3 is pray equal to zero, okay? Now, um, like I said, we have the same thing here and here. Let's factorize that. So if we should bring out m minus 3, okay, open brackets, when this is divided. By this, these brackets will remain as they are, so we have m squared plus 3m plus 9 now when this is divided by this 5, the remainder will be so, plus 5 is equal to zero. All right, permit me to clean this. because we need that space, okay. All right, now we can write m minus 3 multiplied by m cubed plus 3m plus 14 equals zero; now we can express this to be equal to This bracket must also be equal to zero, so we can say that m minus 3 equals zero. and that m cubed plus 3m plus 14 is also equal to zero; now let's solve this side From here we can see that m can be said to be equal to 3 because minus 3 moves over to become plus 3, and this is the first value of our m. Now for this, we are going to note that if we compare this with the ideal quadratic equation, we have a to be equal to one the coefficients of m cubed we have b equal to three, the coefficients of m and we have c equal to 14, which is our constant; now we are going to use the quadratic the equation formula to solve this is the one that states that m will be equal to minus b plus or minus the square root of b squared minus 4ac, all divided by 2a, okay, so that means that m is equal to minus 3 plus or minus square root of 3 squared minus 4 multiplied by 1 multiplied by 14 everything divided by 2 multiplied by 1, so that is exactly what we are going to do get if we substitute these values into this particular equation now if this is the first The moment you've seen this page, you've already seen this amazing channel—please hit the subscription button. Turn on your notification bell so I'll be notified anytime I upload a new video I upload videos every day, sometimes two or three times a day, so feel free to tune in at any convenient time. time to watch our video, please give us a thumbs up—it means a lot to us if you're Actually enjoying this video right now, let's go. So if we solve this, we have m is equal to minus 3 plus or minus square root of 9 minus 4 times 4 is 16 rice is carry 1 4 times 1 4 times 1 is 4 plus that 1 is 5, so this is 56 divided by 2 times 1, we still get 2, so our m is equal to minus 3 plus or minus 9 minus 56 we get 47 plus or minus square root of minus 47 okay divided by 2. Now, when you look at this minus 47, we cannot simplify it any further, right? So that simply means that the second value of our m, I'd like you to sit back and see how we proved that the answer Yes, okay, so m₂ should be minus 3 plus the square root of minus 47 divided by 3, and our m₃ is equal to minus 3 minus square root of minus 47 divided by 3 now let's check and be sure that the answer We have it correct, so allow me to clean this up. We have m, okay? Noted: m is equal to 3, the real value. and the other ones, okay, now we have m equal to 3, right? So 3 to the power of 3 plus 5 brackets 3 okay is equal to 42 now 3 to the power of 3 is 9 plus 5 multiplied by sorry 3 to the power of 3 All right, now 5 times 3 is 15, which is equal to 42, and this plus this is 42. So we have that 42 is equal to 42. Thank you so much for watching. Bye.