A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Can someone help me with an algerba 1 question?
anonymous
 one year ago
Can someone help me with an algerba 1 question?

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The question is Factor completely 2x3y4 − 8x2y3 + 6xy2.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so bassicaly find the GCF

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(2x^3y^4 − 8x^2y^3 + 6xy^2\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The notes that i took in class says that first i need to find a number that goes into all three coeffiecent evenly which is 2

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Step 1 of factoring: Try to factor a common factor. What is the largest common factor of all three terms?

diamondboy
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442526155297:dw

diamondboy
 one year ago
Best ResponseYou've already chosen the best response.0can you go on from this?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Correct. The number part of the GCF is 2. Now you need the variable part of the GCF.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay it said start with a varible with the lowest degree i dont know what that means is the the exponent?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1442526095341:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Degree of a variable is the exponent. You are correct.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay but both x and y have an exponet that is the same

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Below, I broke up the numbers into their factors. You can see clearly (the red helps) that the only number factor all three terms have is 2. \(\color{red}2\cdot x^3 \cdot y^4 − \color{red}2\cdot 2 \cdot 2 \cdot x^2y^3 + \color{red}2 \cdot 3 \cdot xy^2\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes i understand that :)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now let's look at the variables to see what variables appear in all factors. \(\color{red}2\cdot x \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y − \color{red}2\cdot 2 \cdot 2 \cdot x \cdot x\cdot y \cdot y \cdot y + \color{red}2 \cdot 3 \cdot x \cdot y \cdot y\) Normally, you don;t have to do what I did above, but I just want you to see what the exponents really mean. Now we see how many x's and y's are in common to all terms.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so which ever one has the less is the one you need?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(\color{red}2\cdot \color{green}x \cdot x \cdot x \cdot \color{purple}{y \cdot y} \cdot y \cdot y − \color{red}2\cdot 2 \cdot 2 \cdot \color{green}x \cdot x\cdot \color{purple}{y \cdot y} \cdot y + \color{red}2 \cdot 3 \cdot \color{green}x \cdot \color{purple}{y \cdot y}\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Yes. Since the 3rd term only has one x, and the other terms have more than one x, the three terms have only 1 x in common. Since the third term has only 2 y's, and the other terms have more than 2 y's, all three terms have only 2 y's in common.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so 2x? is what your dividing everything by?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Every term has a factor of 2. Every term has a factor of x Every term has a factor of y^2 The GCF is 2xy^2 We divide all three terms by 2xy^2 Now we pull out the common factor, 2xy^2.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Correct. Use 2xy^2.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay imma try to see if i can fiqure i out and tell me if im right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.02xy2(x2y2 − 4xy + 3)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(2xy^2(x^2y^2  4 xy + 3)\) Excellent. You got the same I did.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We are not done, though.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0AHhhh lol i thought we were

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now think of the product xy as a variable. Let's say xy = z. That means x^2y^2 = z^2

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1If you think of the variables that way, we can make a substitution. Wherever we see xy, we will replace it with z. Then wherever we see x^2y^2 we will replace it with z^2.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we have this: \(=2xy^2(x^2y^2  4 xy + 3)\) After the substitution we have this: \(=2xy^2(z^2  4 z + 3)\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The trinomial in the parentheses is a quadratic trinomial in z. We need to try to factor it.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1To factor a trinomial of the form \(x^2 + ax + c\), you need to find two number that multiply to b and add to a. Our trinomial is of that form, so wee need to try to find two numbers that multiply to 3 and add to 4.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Also i forgot to post the answers. 2(x3y4 − 4x2y3 + 3xy2) 2x(x2y4 − 4xy3 + 3y2) 2xy2(x2y2 − 4xy + 3) Prime

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1According to your choices, we are done, and the answer is C.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much! :D

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Just for completeness, let's just finish factoring because the trinomial is also factorable.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1From now on, it's just extra info. In fact, from the point I began with the substitution it's extra info. Since the two numbers have to multiply to 3, a positive number, the two numbers must be both positive or both negative. Since they need to add to 4, a negative number, the two numbers must contain at least one negative number. The two numbers are 3 and 1 \(=2xy^2(z 3)(z  1)\) Now we substitute xy back for z to get the final complete factorization: \(=2xy^2(xy 3)(xy  1)\)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.