What property do you need to use? Can you demonstrate an example of utilizing factoring to solve equations?

Don't forget to include a quadratic equation

Don't forget to include a quadratic equation

Don't forget to include a quadratic equation

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Hopkins, MN

Hi Harry,

ax^{2} + bx + c = 0 is a quadratic equation where a, b and c are all numbers.

When factoring a quadratic equation you want to find two numbers (z,y) that satisfy the following if a = 1:

- (z)(y) = c
- z + y = b

x + z = 0 or

x + y = 0

Example:

Solve x^{2 }+ 6x + 8 = 0.

(2)(4) = 8 and 2+4 = 6. Therefore the factored form is (x + 2)(x + 4) = 0.

=> x + 2 = 0 => x = -2 OR

x + 4 = 0 => x = -4.

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If a is not equal to 1 then you want to find four numbers (e,d,z and y) that satisfy the following:

- (e)(d) = a
- (z)(y) = c
- (e)(y) + (d)(z) = b

ex + z = 0 => ex = -z and x = -z/e OR

dx + y = 0 =>

Example:

Solve 6x^{2} + 11x + 3 = 0

(2)(3) = 6, (3)(1) = 3 and (2)(1) + (3)(3) = 11, therefore (2x + 3)(3x +1) = 0

2x + 3 = 0 => x = -3/2 OR

(3x + 1) = 0 => x = -1/3

Hope this helps!

Woodland Hills, CA

( X + a) ( X + b) = X^{2} + ( a +b) X + ab (1) ( X + a) 2 = X^{2} + 2aX +a^{2} (2)

( X +a ) ( X -a )= X^{2 -}a^{2} (3)

The 3 above identities are key to factoring quadratic, and finding the roots

The 3 above identities are key to factoring quadratic, and finding the roots

In general every quadratic, trinomial aX^{2} + bX + c is generated by multiplication of 2 binomial (linear) expression in the form of 3 identity given above, and subsequently any given Ttrinomial ( quadratic), can

be factored to binomial factors i.e.( X + a) ( X + b) = X^{2} + ( a +b) X + ab, that is used in evaluation of roots of the quadratic.

, .

In other words identities (1), (2) , ( 3) can work both ways.

given a quadratic like : X^{2} + 7X + 10

here we see that ( a + b) = 7 ab =10

a = 2 b =5 is the answer, therefore X^{2} + 7X + 10 = ( X +2) ( X + 5 )

equation (2) is a special case of (1) where a=b , a+b = 2a , ab=a2

equation (3) is a special case of ( 1) where b = -a, a + ( -a) = 0 , ab = a2

These 3 identities are used in factoring a quadratic.

Equation (1) is factorable if there exists 2 whole number whose sum is ( a+ b), and product =ab.

If the answer of the system of equation is not a whole number, then have to do factoring by competing the square, and come up with a factors of irrational and complex numbers, yielding to Irrational and complex roots .

given a quadratic like : X

here we see that ( a + b) = 7 ab =10

a = 2 b =5 is the answer, therefore X

equation (2) is a special case of (1) where a=b , a+b = 2a , ab=a2

equation (3) is a special case of ( 1) where b = -a, a + ( -a) = 0 , ab = a2

These 3 identities are used in factoring a quadratic.

Equation (1) is factorable if there exists 2 whole number whose sum is ( a+ b), and product =ab.

If the answer of the system of equation is not a whole number, then have to do factoring by competing the square, and come up with a factors of irrational and complex numbers, yielding to Irrational and complex roots .

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