CWORTMA Problem 2: For each set of polynomials a. p(x) = 5x²-3x+1 TELENO 3x +1_q(x) = x-1 Cecc 1. use synthetic division to divide p(x) by q(x) and state the remainder, and 2. use the remainder theorem to compare your findings with part (1). b. p(x) = -4x² + 6x-7 q(x) = x +4 c. p(x) = -x + 4x³ = x+3 g(x) = x − 3 - - Page 1 of 1
A) p(x) = 5x^2 - 3x + 1, q(x) = x - 1
Synthetic Division:
We want to divide p(x) by q(x), which is x - 1. Synthetic division for this case is pretty straightforward.
We first set x - 1 = 0 to find the root: x = 1.
Now, we perform synthetic division:
11 | 5 -3 1
2 | 5 2
3--------------
4 5 2 3
5The result is the quotient 5x + 2 and the remainder 3. So, p(x) = (5x + 2)(x - 1) + 3.
B) p(x) = -4x^2 + 6x - 7, q(x) = x + 4
Synthetic Division:
We want to divide p(x) by q(x), which is x + 4. Synthetic division works similarly:
We first set x + 4 = 0 to find the root: x = -4.
Now, we perform synthetic division:
1-4 | -4 6 -7
2 | 4 -40
3----------------
4 0 10 -47
5The result is the quotient -4x + 10 and the remainder -47. So, p(x) = (-4x + 10)(x + 4) - 47.
C) p(x) = -x^4 + 4x^3 - x + 3, q(x) = x - 3
Synthetic Division:
We want to divide p(x) by q(x), which is x - 3. Synthetic division is used again:
We first set x - 3 = 0 to find the root: x = 3.
Now, we perform synthetic division:
13 | -1 4 0 0 3
2 | -3 3 -9 -27
3---------------------
4 -1 1 3 -9 -24
5The result is the quotient -x^3 + x^2 + 3x - 9 and the remainder -24. So, p(x) = (-x^3 + x^2 + 3x - 9)(x - 3) - 24.
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