Solve using synthetic division (show each step). (a3 +5a2 +14a+16)÷(a+2)

The quotient is 1x^2 + 3x + 8.

Step-by-step explanation:

First:  Please use " ^ " to denote exponentiation:  (a^3 +5a^2 +14a+16).

We are dividing this polynomial by (a + 2).  The equivalent divisor in synthetic division is -2.  We set up this synth. div. as follows:

-2    )    1    5    14    16

                -2    -6   -16

          1      3     8      0

Because the remainder is zero (0), we can safely assume that x  = -2 is a root of (a^3 +5a^2 +14a+16) and that x + 2 is a factor of  (a^3 +5a^2 +14a+16).

The quotient is 1x^2 + 3x + 8.

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".