Use synthetic substitution to determine which of the following is a factor of x3 + 2x2 - 5x - 6.

So the factors of the given polynomial are:

x+1

x+3

x-2

Step-by-step explanation:

There is a theorem for determining the possible rational zeros.

The list comes from putting the factors of the constant over the factors of the leading coefficient.

So possible rational zeros here are just the factors of -6 since the leading coefficient is 1:

So we are going to check the following:

1,-1,2,-2,3,-3,6,-6

Let's try 1.

1 goes on the outside:

1  |   1    2    -5     -6

  |         1      3      -2

  ---------------------------

      1     3    -2         -8

So x-1 is not a factor because it did not give us a remainder of 0 (we got a remainder of -8).

Let's try -1.

-1 goes on the outside:

-1 |   1    2     -5      -6

  |        -1      -1        6

  ---------------------------

     1      1      -6       0

So since we got a remainder of 0, then x+1 is a factor.

Now we can just look at the polynomial . This was the other factor we found when we divided our original polynomial by .

is actually factorable.

The coefficient is x^2 is 1. This means all you have to do is find two numbers that multiply to be -6 and add up to be 1.

Hopefully when you read this you thought of 3 and -2.

3(-2)=-6

3+(-2)=1

So the factored form of is .

So the factors of the given polynomial are:

x+1

x+3

x-2

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)