Given that f(x)=9x^2−50, apply the Remainder Theorem to find the remainder of (9x^2−50)÷(x−7/3).
-29
-1
-203/3
-50
To find the remainder of the polynomial division, we can use the Remainder Theorem which states that if a polynomial f(x) is divided by x - c, then the remainder is f(c).
In this case, we are dividing f(x) = 9x^2 - 50 by x - 7/3.
By applying the Remainder Theorem, we substitute x = 7/3 into the polynomial f(x):
f(7/3) = 9(7/3)^2 - 50
= 9(49/9) - 50
= 49 - 50
= -1
Therefore, the remainder of (9x^2 - 50) ÷ (x - 7/3) is -1.
To find the remainder using the Remainder Theorem, we divide the polynomial f(x) = 9x^2 - 50 by the linear divisor x - 7/3.
First, we set up the division:
(9x^2 - 50) ÷ (x - 7/3)
Next, we perform long division:
________________________
(x - 7/3) | 9x^2 + 0x - 50
To start, we divide the first term 9x^2 by x, which gives us 9x. We write this quotient above the horizontal line and multiply it by the divisor:
9x
________________________
(x - 7/3) | 9x^2 + 0x - 50
- 9x^2 + 7x
__________
- 7x - 50
Next, we bring down the next term, which is 0x, and divide it by x:
9x - 7
________________________
(x - 7/3) | 9x^2 + 0x - 50
- 9x^2 + 7x
__________
- 7x - 50
+ 7x - 49
__________
-99
We continue this process until we have no more terms to bring down. In this case, there are no more terms, and the remainder is -99.
Therefore, the remainder of (9x^2 - 50) ÷ (x - 7/3) is -99.