Question

Solve the following equations by either factoring or completing the square:
x^2-4x+3=0

Answer 1

(x-3)(x-1)

Answer 2

(x-3)(x-1)=0
x=3 or 1

Answer 3

can you show me how you got that?

Answer 4

do you know how to multiply the polynomials together?

Answer 5

like (x+a)(x+b)

Answer 6

yeah.

Answer 7

Quick Solution:
x^2-4x+3=0
x^2-3x-1x + 3 = 0
x(x-3)-1(x-3) = 0
(x-3)(x-1) = 0

x = 1,3

Long Solution:
When given an equation of the form ax^2 + bx + c = 0 and asked to find x, perform the following general steps:

1. Find two numbers that multiply to get a*c, yet add to get b. In this case, find two numbers that multiply to get 3, yet add to get -4. The two numbers are -3 and -1.

2. Split the middle term, -4x, into two terms using the two numbers that you found:

x^2 -3x -1x + 3 = 0

Notice that -3x - 1x = -4x

3. Factor the first two terms, then factor the last two terms such that the remaining terms are two identical binomials:
x(x-3) -1(x-3) = 0

4. Factor out the remaining binomial to create the product of two binomials:

(x-3)(x-1) = 0

5. Use the zero product property (ab = 0) to create two separate equations, then solve for x:

x - 3 = 0
x - 1 = 0

x = 3
x = 1