Learn how to solve quadratic equations like (x-1)(x+3)=0 and how to use factorization to solve other forms of equations.
Log in Amber Lynn 8 years agoPosted 8 years ago. Direct link to Amber Lynn's post “In the above equation 3x^...” In the above equation 3x^2+11x-4 = 0, I understand where we need to find two numbers were a+b need to equal 11 to satisfy the 11x, however, I'm having trouble connecting where -12 came from where it states that we need to find numbers to satisfy (a)(b) = -12. I'm seeing a -4 at the end of the equation. Not sure where -12 came from. Was it from multiplying -4 to the co-effiecient of the 3 in 3x^2? • (47 votes) Johnathan 8 years agoPosted 8 years ago. Direct link to Johnathan's post “In the standard form of q...” In the standard form of quadratic equations, there are three parts to it: ax^2 + bx + c where a is the coefficient of the quadratic term, b is the coefficient of the linear term, and c is the constant. The -4 at the end of the equation is the constant. This hopefully answers your last question. Now, your first question. So the problem is that you need to find two numbers (a and b) such that the sum of a and b equals 11 and the product equals -12. Correct? Correct indeed. I use a pretty straightforward mental method but I'll introduce my teacher's method of factors first. What you need to do is find all the factors of -12 that are integers. Let's start with 1. If you misunderstand something I said, just post a comment. (35 votes) Jose Santizo 8 years agoPosted 8 years ago. Direct link to Jose Santizo's post “Sometimes I don't underst...” Sometimes I don't understand some of the problems. :( • (23 votes) ChrisTry162 8 years agoPosted 8 years ago. Direct link to ChrisTry162's post “Just always remember to s...” Just always remember to simplify the expression before u do anything and then make one side equal to zero my subtracting or adding etc. Its easy once u get the hang of it. (22 votes) Clark Burch 10 months agoPosted 10 months ago. Direct link to Clark Burch's post “still confused” still confused • (12 votes) Kim Seidel 10 months agoPosted 10 months ago. Direct link to Kim Seidel's post “Think about what is confu...” Think about what is confusing you. 2) If you are ok with the factoring, then what pay close attention to the other topics on the page. They cover the other steps you need to do in quite some detail. (13 votes) Cooky_0901 10 months agoPosted 10 months ago. Direct link to Cooky_0901's post “I don't get 3x^2-9x-20=x^...” I don't get 3x^2-9x-20=x^2+5x+16. What do we do in the first place? • (3 votes) Kim Seidel 10 months agoPosted 10 months ago. Direct link to Kim Seidel's post “Before trying to factor, ...” Before trying to factor, you need to put the equation in the standard form: Ax^2+Bx+C=0. To do this, use opposite operations to move each term on the right side to the left side. Then factor. Hope this helps. (12 votes) gmblim 6 years agoPosted 6 years ago. Direct link to gmblim's post “In the above equation 3x^...” In the above equation 3x^2+11x-4 = 0, I understand where we need to find two numbers were a+b need to equal 11 to satisfy the 11x, however, I'm having trouble connecting where -12 came from where it states that we need to find numbers to satisfy (a)(b) = -12. I'm seeing a -4 at the end of the equation. Not sure where -12 came from. Was it from multiplying -4 to the co-effiecient of the 3 in 3x^2? • (4 votes) Kim Seidel 6 years agoPosted 6 years ago. Direct link to Kim Seidel's post “Yes, the -12 comes from m...” Yes, the -12 comes from multiplying -4 with the 3 from 3x^2. (7 votes) Danny 8 years agoPosted 8 years ago. Direct link to Danny's post “I know this is not relate...” I know this is not related to the above questions, but i could not find where to ask normal day to day questions. If someone could please help me answer this would be great.: • (1 vote) Vu 8 years agoPosted 8 years ago. Direct link to Vu's post “Expand the squares, then ...” Expand the squares, then distribute the 9. Combine like terms then factor. Post comment if you still feel stuck. (14 votes) Anushka 5 years agoPosted 5 years ago. Direct link to Anushka's post “How do you factor it when...” How do you factor it when the leading coefficient is more than 1? For example, something like 3xsquared+ x-2. • (4 votes) Kim Seidel 5 years agoPosted 5 years ago. Direct link to Kim Seidel's post “You factor the trinomial ...” You factor the trinomial by grouping. See the lessons at this link: https://www.khanacademy.org/math/algebra/polynomial-factorization#factoring-quadratics-2 Hope this helps. (3 votes) Laney 4 years agoPosted 4 years ago. Direct link to Laney's post “My equation is x^2-2x+1=0...” My equation is x^2-2x+1=0 ( find x) How do i factor out the 1? Could i make it 1^2? • (4 votes) Kim Seidel 4 years agoPosted 4 years ago. Direct link to Kim Seidel's post “You need 2 factors of 1 t...” You need 2 factors of 1 that add to -2. (3 votes) 💎Chυcκ Lørrε💎 6 years agoPosted 6 years ago. Direct link to 💎Chυcκ Lørrε💎's post “I figure out that when A+...” I figure out that when A+B=[some number] and AB=[some number] combines, it could be an linear equation. But I don't know how to solve it, because when I'm solving it, a new quadratic equation comes out! For example: • (3 votes) p.m. 6 years agoPosted 6 years ago. Direct link to p.m.'s post “That's a confusing way to...” That's a confusing way to factor, because as you noticed it just results in another quadratic equation. It's easier to just try to think of 2 numbers that add to 3 and multiply to -10, than actually solve it. You could also use the quadratic equation, which always works, so you don't have to try to guess the factors. However, this often takes longer, and if the numbers are simpler you should factor instead. (1 vote) R Dunkin a month agoPosted a month ago. Direct link to R Dunkin's post “Why do the numbers attach...” Why do the numbers attached to the x disappear? for example: x^2 -20x + 100 = 0 • (1 vote) Kim Seidel a month agoPosted a month ago. Direct link to Kim Seidel's post “Think about factors of nu...” Think about factors of numbers. 132 has factors of 11*12. Yet, the original number contains a 3. Where did it go? It only shows up if you multiply the factors. The same is true for factors of quadratics or other polynomials. Hope this helps. (4 votes)Want to join the conversation?
1 * -12
2 * -6
3 * -4
4 * -3
6 * -2
12 * -1
Here we see 6 factor pairs or 12 factors of -12. Let's see which one adds up to 11. It seems like 12 + (-1) = 11. So we'll split 11 to 12 and -1.
My other method is straight out recognising the middle terms. This works well with small numbers. I can clearly see that 12 is close to 11 and all I need is a change of 1. So that leaves out 12 * -1 and -12 * 1. I can see that -12 * 1 makes -11 which is not what I want so I go with 12 * -1.
1) Is it the factoring? If it is, you need to review the lessons and practice problems for factoring. There are multiple factoring techniques. You need to know each of them and when to apply them.
Factorise the expression as far as possible to prime factors:
(x-1)^2-9(y-1)^2 ...
^2(power of 2)
Your choices are to use: 1*1 or (-1)(-1). Which pair adds to -2?
Hope this helps.
Problem:
Factoring x²+3·x-10=(x+a)(x+b)
Linear equation:
①a+b=3
②a·b=-10
Solve:
a=3-b
Substitute 3-b into equation ②
(3-b)b=-10
3·b-b²=-10
And I don't know how to solve.
(x-10)^2 Where did the -20x go?
Multiply (x-10)^2 and you will recreate the -20x.
(x-10)^2 = (x-10)(x-10) x^2-10x-10x+100 = x^2-20x+100
