Learn how to factor a common factor out of a polynomial expression. For example, factor 6x²+10x as 2x(3x+5).
Log in Ed cole 7 years agoPosted 7 years ago. Direct link to Ed cole's post “i'm having trouble with t...” i'm having trouble with this specific problem (our teacher didn't explain it well) • (17 votes) David Severin 7 years agoPosted 7 years ago. Direct link to David Severin's post “So first, we have a = 5, ...” So first, we have a = 5, b = 21, and c = -20. ac = 5*-20 = - 100. Since this product is negative, I need two numbers which multiply to be -100 and add to be 21, but with a negative product, I can really say two numbers that multiply to be 100 and subtract to be 21, and since the 21 is positive, the bigger number has to be positive. So this is easy to guess: 25 - 4 = 21. Thus, we have the middle term broken into two parts, 21m = 25m - 4m. So our equation could be changed to 5m^2 +25m - 4m - 20 = 0. The GCF of the first two is 5m, and of the last two is -4, so 5m ( m + 5) - 4 (m + 5) = 0, we have a common factor of m + 5, so pulling that out, we get (5m - 4)(m + 5) = 0. Set the first equal to zero to get m = 4/5 and the second equal to zero to get m = -5. (68 votes) jujumont333 8 years agoPosted 8 years ago. Direct link to jujumont333's post “#7 even when I put in the...” #7 even when I put in the answer given by the help button, it didn't work no matter how many times I tried it. • (17 votes) Kayo OPS14 5 years agoPosted 5 years ago. Direct link to Kayo OPS14's post “It was fine when I did it...” It was fine when I did it. Use the controls underneath the answer box to assist you, they help. (11 votes) 4 years agoPosted 4 years ago. Direct link to Child's post “I seriously need help. I'...” I seriously need help. I've learned factoring only once before today, and I still don't really get it. I mean I do, but I don't. I understand when the terms are broken down, like how 2x^2 is also 2*x*x. That's easy. It's mostly the finding the second term part, and making sure everything is in the right order. I know this is kind of a vague plea for assistance, but I don't know how else to explain my jumbled brain. • (14 votes) A/V 4 years agoPosted 4 years ago. Direct link to A/V's post “Factoring is like breakin...” Factoring is like breaking down two cakes and trying to take out the layers that are the same. lackluster analogy but the base of what you know (2x² = 2*x*x) is essential. Let's start with a binomial, (4x²+8x) It seems that the biggest term that goes into both 4x² and 8x is 4 and x. Multiple 4 and x together to get 4x. It's also good to notice that the other x is 4x² is not included. That's because theres only 1 x in 8x. We would put the other x in if it were 8x², but it is not. Trinomials are the same process but with more terms. hopefully that helps and if you want an example for trinomials lmk ! (23 votes) Grace Muriithi 8 years agoPosted 8 years ago. Direct link to Grace Muriithi's post “On question 4, I typed in...” On question 4, I typed in the wrong answer, then it said it was wrong. Then, I put in the right answer and it says it is still wrong! Why? Please fix! • (11 votes) BethanyVemulapalli 5 years agoPosted 5 years ago. Direct link to BethanyVemulapalli's post “So this isn't really on t...” So this isn't really on this page but I don't know where else to ask it. I have some homework that I don't fully understand a similar problem to the one I am confused on is 15x(x+6)^2+45x(x+6)+35 • Avery Baker 4 years agoPosted 4 years ago. Direct link to Avery Baker's post “I have the following prob...” I have the following problem 6x^3 + 8x^2 - 4x but I can't get it right can someone help me, please. • (8 votes) A/V 4 years agoPosted 4 years ago. Direct link to A/V's post “So let's begin with GCF. ...” So let's begin with GCF. Looking at the polynomial, it seems that 2x is the GCF of that. Let's take that out: 2x(3x²+4x-2) Noticing that there is a trinomial that might factor, we use the technique: Noticing that all factors of 6 cannot add up to 4, we leave it at that. In some cases you cannot factor a trinomial, and this is an example of such. Answer: 2x(3x²+4x-2) (8 votes) jacorijay 4 years agoPosted 4 years ago. Direct link to jacorijay's post “how do I factor x^2-36?” how do I factor x^2-36? • (7 votes) happypelican 4 years agoPosted 4 years ago. Direct link to happypelican's post “x^2-36 factors into (x+6)...” x^2-36 factors into (x+6)(x-6). It's in the form a^2-b^2, which in factored form is (a+b)(a-b). (7 votes) Annie Giampietro 8 years agoPosted 8 years ago. Direct link to Annie Giampietro's post “The hint for number 7 is ...” The hint for number 7 is tricking me can you send a different hint • (2 votes) Revika 3 years agoPosted 3 years ago. Direct link to Revika's post “factors of (a+b)^3 - (a-b...” factors of (a+b)^3 - (a-b)^3 • (4 votes) Jerry Nilsson 3 years agoPosted 3 years ago. Direct link to Jerry Nilsson's post “Using the binomial theore...” Using the binomial theorem, we get Combining like terms, we get Finally, we factor out 2𝑏, which gives us (5 votes) Golden Pig 6 years agoPosted 6 years ago. Direct link to Golden Pig's post “A few problems are tellin...” A few problems are telling me to factor out multiple binomials in a single problem, such as x^2 - y^2 + 7x + 7y. I know the first step is to split the problem into multiple binomials (so that the problem then becomes (x^2 - y^2)+(7x + 7y), but I don't know how to make a GCF of two different variables with the same power. How would you be able to do that? • (3 votes) VVCephei 6 years agoPosted 6 years ago. Direct link to VVCephei's post “`x` and `y` don't have an...” (8 votes)Want to join the conversation?
5m^2+21m-20=0
I am supposed to solve it using factoring, nothing else.
The main part of factoring is to find the G reatest C ommon F actor. What common factors does 4x² and 8x? Breaking it down,
4 ⋅ x ⋅x = 4x²
2⋅4 ⋅ x = 8x
Let's now take out 4x from 4x²+8x :
4x(x+2) = 4x²+8x through the distributive property.
a * c = -6
a + c = 4
(𝑎 + 𝑏)³ − (𝑎 − 𝑏)³
= 𝑎³ + 3𝑎²𝑏 + 3𝑎𝑏² + 𝑏³ − (𝑎³ − 3𝑎²𝑏 + 3𝑎𝑏² − 𝑏³)
6𝑎²𝑏 + 2𝑏³
2𝑏(3𝑎² + 𝑏²)x and y don't have any common factors between themselves. But x²-y² is a difference of squares:x² - y² = (x - y)·(x + y)
And 7x+7y have a common factor of 7:7·x + 7·y = 7·(x + y)
So now you have the following expression:(x - y)·(x + y) + 7·(x + y)
Notice that you can factor (x + y) out:(x + y)·((x - y) + 7) = (x + y)·(x - y + 7)
And that's it.
