How to factorize a quadratic equations?

Question

I need a complete step-by-step on how to factorize a quadratic equations because i'm totally clueless about it.And please make it very simple to for me understand.Thanks...

Answer 1

Try these, I hope they help you

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Let's look at an example: x² + 6x + 8 = 0.
We can rewrite it as x² + 2x + 4x + 8 = 0.

We can factorise this into two terms: x (x + 2) + 4 (x + 2) = 0.
Notice that (x + 2) appears twice: it is a common factor!

We can factorise the expression further to: (x + 4)(x + 2) = 0
giving the correct solutions: x=-4 and x=-2.

You may have spotted that 4 + 2 = 6 and that 4 × 2 = 8.

Similar quadratic equations can be factorised and solved if the number on its own (c in the standard equation) has factors that add up to b (the number of x's).
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Solving quadratic equations by factorising.

If we have two numbers, A and B, such that AxB = 0, then it must follow that either A = 0, or B = 0 (or both), because when we multiply any number by 0, we get 0.

In intermediate algebraic manipulation, you revised how to factorise (put into brackets) a quadratic expression such as x2 - 9x + 20 - we are looking for two numbers which multiply to give +20 and add to give -9.

Have a look at this question where you need to solve a quadratic equation by factorising.
Question 1

Solve the equation x2 -9x + 20 = 0
The Answer

This solution will help you with the answer:

1. If we have a quadratic equation x2 -9x + 20 = 0, then it follows that (x - 4) (x - 5) = 0

2. So we have two brackets multiplied together, and the answer is 0. Either (x - 4) = 0 OR (x - 5) = 0

3. So x = 4 or x = 5 (solving these two simple equations).

4. We could check these answers:
42 - 9x4 + 20 = 16 - 36 + 20 = 0
52 - 9x5 + 20 = 25 - 45 + 20 = 0

You try this question.
Question 2

Solve the equation x2 + 8x + 15 = 0
The Answer
x = -3 or x = -5?



If you were struggling with the answer, try to fill in the blanks below.

Write down the quadratic equation.
x2 + 8x + 15 = 0

We want two numbers which multiply to give ? and add to give ?...
3 and 5

Write the equation with brackets.
So (x + ?)(x + ?) = 0

Work out how to make 0 from the brackets.
So either x + 3 = 0 or x + ? = 0

The answers are:
x = -3 or x = -5.

Check:
(-3)2 + 8x(-3) + 15 = 9 - 24 + 15 = 0, (-5)2 + 8x(-5) + 15 = 25 - 40 + 15 = 0

Answer 2

Let's say you have an equation like
x^2+5x+6=0
What you want to do is get the factors of 6.
To do that, you get:
1*6=6
2*3=6, so your factors are 1,2,3 and 6.
Notice that your middle term is 5x. You want to use the factors that will give you a sum of 5x when you multiply out the equation.
so we try 1*6 and we will get,
(x-1)(x+6). When you multiply it out, you will get
x^2+6x-x-6. Breaking it down further,
x^2+5x-6. We see that this is wrong because the equation is +6 and not -6. It is all trial and error. Since this did not work, we could try the other factor, which is 2*3 and we get.
(x+2)(x+3). Multiplying it out, we get
x^2+3x+2x+6. Breaking this down further, we get
x^2+5x+6. This is the correct answer. You can try this web site for more examples: http://www.purplemath.com/modules/solvquad.htm
You basically have to practice a lot to get the hang of it because each problem will present its own unique twist, but once you get it, you'll never forget it.

Answer 3

I don't think anybody (especially if your teachers haven't succeeded in doing so) is going to be able to teach you how to factor quadratic equations through yahoo answers.

I'd suggest asking a peer from your math class or letting the teacher know you would like extra help. If you would rather do it independently then you should look up examples of this being done online.

Gl.

Answer 4

Rather than give a lot of theory , I think we should consider the two examples given below:-

Example 1
x² + 5x + 6
= (x -------).(x---------) gives x² term
=(x ------ 3).(x---------2) gives 6 term
Now consider inner product of 3x and outer product of 2x and decide upon signs to be used to obtain sum of + 5x and product of +6
= (x + 3).(x + 2) is answer
Check
x.(x + 2) + 3.(x + 2) = x² + 2x + 3x + 6
= x² + 5x + 6 as required

Example 2
x² - 8x + 7
= (x-----).(x-----)
= (x----7).(x----1)
= (x - 7).(x - 1)
Check
x.(x - 1) - 7.(x + 1)
= x² - x - 7x - 7
= x² - 8x - 7

Hope these might help.

Answer 5

I agree with leiter_1 answer. But I give it a try.


To factor quadratic equations,

You have to use the FOIL method

Tip: Study, study and study it more.


Go here http://www.freemathhelp.com/using-foil.html

Answer 6

I think that there must be a mistake in the question if your supposed to factorise it, there is no way of factorising it in the for (x+a)(x+b), the answer for the question comes out as X = 1+1.414i or 1-1.414i so unless your daughter is doing complex numbers then the question is wrong. Hope that helps :)