How to factorise quadratrics when a=1

Updated: 8/30/2020

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- Hello
- Hi, Can i help you?
- Yes. Actually,I wanted to ask how to factor quadratics when a=1
- Actually, yes.i wanted to know how to factore quadratics when a=1
- Ok. That is simple.
- Ok,
- Lets take this example. x^2+5x+6. we have to figure out the same two numbers that can give us 5 when added together and 6 when multiplied. the two numbers that come to mind to me are 3 and 2. so we know the factored form is (x+2)(x+3). Do you understand?
- Then we look at the original equation and think of two numbers that if we add them it will give us the corresponding b and if we multiply them it was give us the corresponding c. Then we distribute them one at a time and then get the factored form.
- Ok. Can I try an example?
- So to do this. we know the quadratic form is ax^2+bx+c. To factor,we write it in the form of (x+ )(x+). since quadratics are always at the power of 2. we put an x in each bracket.
- Ok i think I understand. can you give me an example to try on my own?
- Sure. Let's do this one:x^2+13x+40
- Now, the two numbers that come to mind are 8 and 5 since 8x5=40 and 8+5=13. so the factored form is (x+8)(x+5). Is this correct?
- Just like you said since we have a quadratic. it is to the power of 2. Thus we write it in the form of (x+ )(x+ ). Next, we have to find two two numbers that will give me 13 and 40 when added and multiplied respectively.
- So far, so good.
- Yes and it's all because of your wonderful explanation. Thank you very much.
- Good job . Seems like you understand completely.
- alright so first i'll write the form (x+ )(x+ ) since it is to the power of 2 we have two x's. Then i think of two numbers in which the adding them gives me 8 and multiplying them gives me 40.