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what is this factoring method?

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I have this method for factoring quadratic equations, but I don't remember what it was called. Maybe someone here knows?

Here's an example of how it's used:

The equation: 24=10x^2-22x
After converting to standard form: 10x^2-22x-24=0

1. Multiply the coeffiecient of the first term with the last term and find factors that add up to the middle term. 10x24=240=30x8 and -30+8=22

2. Replace the middle term with the two factors. 10x^2-30x+8x-24=0

3. Factor out the greatest common multiple. 10x(x-3)+8(x-3)=0

4. Regroup. (10x+8)(x-3)=0

5. Solve for x. x=-0.8 or x=3

This was in my math textbook last year so it should be widely used, but I can't find it in my current math book. What's the name for this method Shocked

Shocked

? Thanks in advance.

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Re: what is this factoring method?

lil_cat_luver wrote:

I have this method for factoring quadratic equations, but I don't remember what it was called. Maybe someone here knows?

Here's an example of how it's used:

The equation: 24=10x^2-22x
After converting to standard form: 10x^2-22x-24=0

1. Multiply the coeffiecient of the first term with the last term and find factors that add up to the middle term. 10x24=240=30x8 and -30+8=22

2. Replace the middle term with the two factors. 10x^2-30x+8x-24=0

3. Factor out the greatest common multiple. 10x(x-3)+8(x-3)=0

4. Regroup. (10x+8)(x-3)=0

5. Solve for x. x=-0.8 or x=3

This was in my math textbook last year so it should be widely used, but I can't find it in my current math book. What's the name for this method ? Thanks in advance.

Hey,

Hmmm thats tough .... Its been QUITE a while ....

I know names of 3 methods of factoring Quadratic Equations:

If quadratic equation is of form ax^2+bx+c = 0

1. Coefficient Factorization Method:

We find 2 factors p,q of a*c such as

a*c = p*q

So c = pq/a

& p+q = b

then we rearrange as

ax^2 + px + qx + pq/a = 0

ax(x + p/a) + q(x + p/a) = 0

(ax+q)(x+p/a)=0

x = -q/a

or x = -p/a

Here is where your method belongs

2. Completing the Square:

Rearrange ax^2 + bx = -c

x^2 + (b/a)x = (-c/a)

x^2 + 2(b/2a)x +(b/2a)^2 = (-c/a) + (b/2a)^2

(x + b/2a)^2 = (-4ac+b^2)/4a^2

x + b/2a = +- sqrt((b^2-4ac)/4a^2)

x = +- sqrt(b^2-4ac)/2a - b/2a

x = (-b +- sqrt(b^2-4ac)) / 2a

3. The Quadratic Formula:

Directly Use x = (-b +- sqrt(b^2-4ac)) / 2a

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The second method, I think I learned it last year and it was called the "crazy method" according to the math teacher, haha. Now I know the actual names for both of them Very Happy

Very Happy

Thank you!

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The method you expounded starts with the quadratic expression "ax^2 + bx + c", and uses the values of "a", "b", and "c" to figure out the factors. Hence, a common name for this method is "the a-b-c method".

Eliz.

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try this
10x^2-22x-24=0
so divide by 2
5x^2-11x-12=0
assumming an even factor and because 5 is prime this becomes
5x^2-11x-12=(x+a)(5x+b)=5x^2+(5a+b)x+ab=0
so
5a+b=-11 and ab=-12
make the following table from ab=-12 with constraqint that 5a+b=-11
a b ab 5a+b
-1 12 -12 -5+12=7
-2 6 -12 -10+6=-4
-3 4 -12 -15+4=-11
so a=-3 and b=4
put into
(x+b)(5x+b)=0 and check
(x-3)(5x+4)=0
5x^2-15x+4x-12=0
5x^2-11x-12=0
multiply factors by 2
10x^2-22x-24=2(x-3)(5x+4)=0

Rap

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Thanks you Eliz Mr. Green

Mr. Green

Rap, your method confuses me a little, but it's probably because I'm not used to reading math equations on a computer screen Confused

Confused

...I'll come back and read it again later.

Thanks to everybody Very Happy

Very Happy

I got so much info and all I wanted was a name Razz

Razz

0 Replies

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