Divide g(x)=3x^2+4x-5 by x - 7 to find g(7)
To divide g(x) = 3x^2 + 4x - 5 by x - 7, we can use long division.
First, let's write out the long division:
3x + 25
x - 7 | 3x^2 + 4x - 5
The first step is to divide the leading term of the numerator by the leading term of the denominator. In this case, (3x^2) / (x) = 3x. Write this above the division line.
3x + 25
x - 7 | 3x^2 + 4x - 5
-(3x^2 - 21x)
Next, multiply the divisor (x - 7) by the quotient in the previous step (3x) and write the result below the line.
3x + 25
x - 7 | 3x^2 + 4x - 5
-(3x^2 - 21x)
--------------
25x
Subtract the result obtained above from the numerator (specifically, subtract 25x from 4x - 5) and write the result below the line.
3x + 25
x - 7 | 3x^2 + 4x - 5
-(3x^2 - 21x)
--------------
25x + 0
- (25x - 5)
Simplify further:
3x + 25
x - 7 | 3x^2 + 4x - 5
-(3x^2 - 21x)
--------------
25x + 0
- (25x - 5)
--------------
5
The final result is a remainder of 5. Therefore, g(7) = 5.