If p(u)=7u2–6u–40, use synthetic division to find p(2).
p(u) = 7 u^2 – 6 u – 40
if u = 2
p = 7 * 4 - 6 * 2 - 40
= 28 -12 - 40
= -24
I have no idea what this has to do with division, synthetic or otherwise.
google synthetic division and you will find many examples and videos.
There are also synthetic division calculators which will show all the steps.
You can check your answer by using the remainder theorem.
The remainder when dividing by u-2 is p(2) = -24
I just started to learn this and I don't have a good grasp on it yet if you do it can you explain it too
To find the value of p(2) using synthetic division, we need to follow these steps:
Step 1: Write down the coefficients of the polynomial in descending order. In this case, the polynomial is p(u) = 7u^2 - 6u - 40. So, the coefficients are 7, -6, -40.
Step 2: Set up the synthetic division table by writing down the divisor, which is u - 2. (Note: We use u - 2 since we want to find p(2), and substituting 2 into the polynomial gives u - 2 as the factor.)
2 | 7 -6 -40
Step 3: Bring down the first coefficient, which is 7, into the first row of the synthetic division.
2 | 7 -6 -40
|_________
7
Step 4: Multiply the divisor, u - 2, by the number in the bottom row (which is 7) and write the result below the second coefficient.
2 | 7 -6 -40
|_________
7
-----
Step 5: Add the value in the second row to the corresponding coefficient, which is -6.
2 | 7 -6 -40
|_________
7
-----
2
Step 6: Repeat steps 4 and 5 until you reach the last coefficient.
2 | 7 -6 -40
|_________
7
-----
2
4
---
0
Step 7: The number in the bottom row of the synthetic division table is the remainder. Since the remainder is 0, it means that (u - 2) is a factor of the polynomial.
Step 8: The result of the synthetic division is the coefficients of the quotient, which corresponds to the polynomial without the remainder. In this case, the quotient is 7u + 4.
Step 9: Finally, substitute 2 into the quotient polynomial, 7u + 4, to find p(2):
p(2) = 7(2) + 4 = 14 + 4 = 18.
Therefore, p(2) equals 18.