Divide g(x)=3x^2+4x−5 by x−7 to find g(7).

Answer 1

To divide g(x) = 3x^2 + 4x - 5 by x - 7, we can use synthetic division.

The rule is to bring down the first term of g(x), which is 3x^2. Put a 0 for the x variable in the division box next to the 3.

7 | 3 4 -5
|_______

Next, multiply the divisor, x - 7, by the result on the top line (which is 3).

7 | 3 4 -5
21

Write the result (21) under the next term of g(x) which is 4x, and add the two terms together.

7 | 3 4 -5
21
________
7 | 3 25 16

Now, multiply the divisor (x - 7) by the result on the top line (which is 25).

7 | 3 4 -5
21
________
7 | 3 25 16
21
________
7 | 3 46 11

Write the result (46) under the next term of g(x) which is -5, and add the two terms together.

7 | 3 4 -5
21
________
7 | 3 25 16
21
________
7 | 3 46 11
42
________
7 | 3 88 53

The result of the long division is:

g(x) = 3x + 46 + 53/(x - 7)

Now, to find g(7), we substitute 7 into the expression for g(x):

g(7) = 3(7) + 46 + 53/(7 - 7)
= 21 + 46 + 53/0

Since division by zero is undefined, g(7) is undefined.