could someone show me how they come up with the answer. x^2-4x+3. It needs to be factored out completely.?

Answer 1

The FOIL method is used when multiplying 2 binomials to come up with a trinomial.

1. The first term of the trinomial is the product of the first terms of the binomials.

2. The last term of the trinomial is the product of the last terms of the binomials.

3. The coefficient of the middle term of the trinomial is the sum of the last terms of the binomials.

4. If all the signs in the trinomial are positive, all signs in both binomials are positive.

Keeping these important things in mind, you can factor trinomials.

First, write down two sets of parentheses to indicate the product.

( )( )

Since the first term in the trinomial is the product of the first terms of the binomials, you enter x as the first term of each binomial.

(x )(x )

The product of the last terms of the binomials must equal 3, and their sum must equal -4. Since the product is positive, either both numbers must be positive or both must be negative.

Two different pairs of factors have a product that equals 3.

(1)(3) = 3 (-3)(-1) = 3

However, only one of those pairs has a sum of -4.

(-3) + (-1) = -4

Therefore, the second terms in the binomial are -3 and -1 because these are the only two factors whose product is 3 (the last term of the trinomial) and whose sum is -4 (the coefficient of the middle term in the trinomial).

(x - 3)(x - 1) is the answer.

Answer 2

(x-3) (x-1)

the answer is either 3 or 1.

remember that two negative numbers are positive... so -3 times -1 equals positive 3.

adding two negative numbers will give you a negative number... so -3 plus -1 equals -4; this is the -4x part.

doing this is guess and check. you have to try certain numbers to get the right factor, but once you get an answer you should check it. Just remember your basic principles and you should be able to get the right answers every time.


Peace.

Answer 3

a=1
b=-4
c=3

D = b²-4ac = 16 - 12 = 4

s1 = [b - square-root(D)] / (-2a) = [-4 -2]/(-2) = 6/2 = 3
s2 = [b + square-root(D)] / (-2a) = [-4 +2]/(-2) = 2/2 = 1

x^2-4x+3 = (x-s1)(x-s2) = (x-1)(x-3)


ps :
try to solve " 2.5 x² + 6.3x + 2.5 = 0 " with the others solutions, below ... it should be very complicated !!!

my solution works every time ... even when D<0 (complex numbers)

FOIL is not the best way to solve equation ... it's work only with easier cases

Answer 4

-8x^2 + 2x^3 + 4x - sixteen first, rewrite it with exponents in descending order 2x^3-8x^2+4x-sixteen 2(x^3-4x^2+2x-8) now rewrite to be certain grouping x^3+2x-4x^2-8 x(x^2+2)-4(x^2+2) (x-4)(x^2+2) x=4, +/-sqrt(-2)

Answer 5

(x-3)(x-1)

Use FOIL:

F-first (x + x)
O-outer (x times -1)
I-inner (-3 times x)
L-last (-3 + -1)