Divide g(x)=3x^2+4x−5 by x−7 to find g(7).
g(7)=
First, let's use polynomial long division to divide g(x) by x-7:
3x + 25
_____________________
x - 7 | 3x^2 + 4x - 5
-(3x^2 - 21x)
_______________
25x - 5
-(25x - 175)
______________
170
Therefore, g(x) = (x-7)(3x+25) + 170.
Now let's find g(7):
g(7) = (7-7)(3(7) + 25) + 170
= (0)(21 + 25) + 170
= 0 + 170
= 170
Therefore, g(7) = 170.
To divide the polynomial g(x) = 3x^2 + 4x - 5 by x - 7, we can use the long division method.
Write the polynomial g(x) and the divisor x - 7:
3x + 11
---------------------
x - 7 | 3x^2 + 4x - 5
Divide the first term of the polynomial g(x) by the first term of the divisor to get the quotient, which is 3x. Write the quotient above the horizontal line:
3x
---------------------
x - 7 | 3x^2 + 4x - 5
Multiply the divisor by the quotient, which gives us (x - 7)(3x) = 3x^2 - 21x. Write this expression below the polynomial g(x):
3x
---------------------
x - 7 | 3x^2 + 4x - 5
- (3x^2 - 21x)
Subtract the expression below from the polynomial g(x) by changing the signs and combine like terms:
3x
---------------------
x - 7 | 3x^2 + 4x - 5
- (3x^2 - 21x)
---------------------
25x - 5
We now have a new polynomial, 25x - 5, which represents the remainder of the division. Since there is no further term in the polynomial, we have completed the long division.
To find g(7), we substitute x = 7 into the original polynomial g(x):
g(7) = 3(7)^2 + 4(7) - 5
= 3(49) + 28 - 5
= 147 + 28 - 5
= 175
Therefore, g(7) = 175.