# Using the quadratic equation x2 – 6x + 8 = 0, perform the following tasks:a) Solve by factoring. Answer:?

• *Multiply the 1st and last coefficient (1*8 = 8). Find two numbers that give you 8 when multiplied and -6 (middle coefficien) when added/subtracted. The numbers are: -2, -4

First: rewrite the equation with the new middle numbers >

x^2 – 2x – 4x +8 = 0

Sec: group “like” terms and factor both sets of parenthesis >

(x^2 – 2x) – (4x +8) = 0

x(x – 2) – 4(x – 2) = 0

(x – 2)(x – 4) = 0

Third: solve for both “x” variables by setting the parenthesis to equal “0” >

x – 2 = 0

x – 2+2 = 0+2

x = 2

x – 4 = 0

x – 4+4 = 0+4

x = 4

(2, 4)

• What does the word factor mean?

If you do not know the definitions of math words, solving questions will not make much sense.

When two integers are multiplied together, the answer is called a product. The integers that were multiplied together are called the factors of the product.

For example:

5 x 6 = 30.

Numbers 5 and 6 are the FACTORS and 30 is the PRODUCT.

When you look for factors, you are looking for the numbers or terms that when multiplied will give you the product.

We Have:

x^2 – 6x + 8 = 0…ORIGINAL QUESTION

(1) Ask yourself: What two numbers when multiplied together will produce 8 BUT when added will produce the middle number, which in your question is -6? See it?

Yes, NEGATIVE 4 times NEGATIVE 2 = 8 but when added = -6.

Is this clear?

(2) WE FACTOR the trinomial.

So, the trinomial x^2 – 6x + 8 becomes (x – 4) (x – 2).

NOTE: (x – 4) is a FACTOR and (x – 2) is the other FACTOR.

(3) Set EACH FACTOR to = 0 and solve for x.

x – 4 = 0

x = 4.

Now, the other factor.

x – 2 = 0

x = 2

Final answer: x = 4 and x = 2.

Do you know what that means?

This means that if you REPLACE x in your original question with 4 or 2, you will get the SAME answer on BOTH sides.

In other words, 4 and 2 are the ROOTS or SOLUTION to your ORIGINAL question.

Is this clear?

Again, final answer: x = 2 and x = 4.

Guido

• X 2 6x 8 0

RE:

Using the quadratic equation x2 – 6x + 8 = 0, perform the following tasks:a) Solve by factoring. Answer:?

• x^2 – 6x + 8 = 0

You expect the factors to look like (x + a)(x + b)

Multiplied out: x^2 + ax + bx + ab

You see that the coefficient of x is the sum of a & b, and the constant term is their product.

(-2)(-4) = + 8

(-2) + (-4) = – 6

x^2 – 6x + 8 = 0

(x – 2)(x – 4) = 0

A true statement when either factor = 0

x – 2 = 0

x = 2

x – 4 = 0

x = 4

Roots are 2, 4

• x^2 – 6x + 8 = 0

To factor, you ask yourself: What two numbers do you multiply to get the constant term (the one without an x), and add to get the middle term (which is the coefficient of x)?

(x + ?) (x + ?)

The two numbers that multiply to get 8 are -4 and -2, and added together they make -6, so those are the two values.

(x – 4) (x – 2) = 0

Now that it is equated to 0, we just individually assign each of them to 0 to get all our solutions.

x – 4 = 0, so x = 4

x – 2 = 0, so x = 2

Therefore, x = {2, 4}

• x2-6x + 8 = 0

x2-6x = -8

x – 3x = -4

-2x = -4

x = 2

2(2) – 6(2) + 8 = 0

4 – 12 + 8 = 0

0 = 0

• x^2-6x+8=0

(x-4)(x-2)=0

x-4=0

x=4

x-2=0

x=2

x=2, 4

• x2 – 6x + 8 = 0

x = Negative 2

• x = 4 and x = 2.

( x – 2) (x – 4) = 0