Factorize 14a³-21a²+7a

Question

It's difficult 

Answer 1

Hi Deekay for New York, NY...hope you had a great day at school.

Great polynomial problem...glad you contacted Wyzant. I am here to help.

I am going to show you how to begin to solve this, and once you learn how you will be a champ at solving them. It beings with the part of Algebra called 'like terms'...remember that??? When a problems asks you to factor [sorry 'factorize' is not a word...but we'll skip that for now]

So now your problem is to factor:   14a³ - 21a² + 7a

You need to look at each of the expressions individually, then determine if there are things that they have in common. Here is an example, very similar and I'll help you understand how to do this. 

Let's say we have the expression?    64d⁵  +  32d⁴  -  16d³  + d²  + 40

   [64d⁵] + [32d⁴] - [16d³] + [40d²]      First we look at each expression

   [64d⁵] + [32d⁴] - [16d³] + [40d²]    Notice each expression has some 

                                                         exponent of dⁿ and the coefficients

                                                         are some multiple of 8. Look for

                                                         less factor and then apply it to

                                                         each of the expressions. In this 

                                                         case, d² is the least common dⁿ

     d²[64d³] + d²[32d²] - d²[16d] + d²[40]    Do you see what we did?

Now we rewrite the expression, moving the d since they all are the same

   d²([64d³] + [32d²] - [16d] + [40])   Now, we know each of the 

                                                         coefficients are multiples of 8, we

                                                         write the expression showing that

   d²([8x8d³] + [8x4d²] - [8x2d] + [8x5]) Notice 8 is in each expression

                                                             Just like we did with d we put it

                                                             on the outside of the brackets

  8d²([8d³] + [4d²] - [2^d] + [5])           Leaving us the coefficients:

                                                               8, 4, 2, 5    Is there anything

                                                          in common with these numbers?

                                                          the answer would be no. so that 

                                                          would be our factor.

   8d²(8d³ + 4d² - 2d + 5)                  This is what our factor would look

                                                        like. To check to see if your answer

                                                        is correct, multiply 8d to each of

                                                        the expressions to see if you get 

                                                        the beginning expression

Now, just follow the example. I know you can do it. Then you will be a pro.

Let me know if you have any further problems, Contact me on Wyzant

Answer 2

14a³ - 21a² + 7a

Always GCF first!

7a(2a² - 3a + 1)

 

Can you continue?