83.) Polynomial Division: (3x^5 - 15x^4 + 4x^3 + 11x^2 - 9x + 2)/ (x^2 - 5x + 2)
Write problem in special format:
x^2 - 5x + 2/ 3x^5 - 15x^4 + 4x^3 + 11x^2 - 9x + 2
Step 1: Divide the leading term of the dividend by the leading term of the divisor: 3x^5/x^2 = 3x^3
Write calculated result in upper part table: Multiply it by the divisor:
3x^3 (x^2 - 5x + 2) = 3x^5 - 15x^4 + 6x^3
Subtract dividend from obtain result:
(3x^5 - 15x^4 + 4x^3 + 11x^2 - 9x + 2) - (3x^5 - 15x^4 + 6x^3)
= - 2x^3 + 11x^2 - 9x + 2
x^2 - 5x + 2/3x^5 - 15x^4 +4x^3 +11x^2 -9x +2 = 3x^5/x^2 = 3x^3
- 3x^5 -15x^4 +6x^3 3x^3 (x^2 - 5x + 2) = 3x^5 - 15x^4 + 6x^3
- 2x^3 +11x^2 -9x +2
Step 2: Divide the leading term of the obtained remainder by the leading term of the divisor: - 2x^3/x^2 = -2x
Write down the calculated result in the upper part of the table: Multiply it by the divisor:
- 2x ( x^2 - 5x + 2) = -2x^3 + 10x^2 - 4x
Subtract the remainder from obtaining results:
( - 2x^3 + 11x^2 - 9x + 2) - ( - 2x^3 + 10x^2 - 4x) = x^2 - 5x + 2
x^2 - 5x + 2/ 3x^5 -15x^4 + 4x^3 +11x^2 -9x +2 = 3x^3 -2x
- 3x^5 -15x^4 +6x^3
-2x3 +11x^2 -9x +2 -2x^3/x^2 = -2x
-2x3 +10x^2 -4x - 2x (x^2 - 5x + 2) = -2x^3 + 10x^2 - 4x
x^2 -5x +2
Step 3: Divide the leading term of the obtained remainder by the leading term of the divisor: x^2/x^2 = 1
Write down the calculated results in the upper part of table. Multiply by the divisor: 1 (x^2 - 5x + 2) = x^2 - 5x + 2
Subtract the remainder from obtained result: (x^2 - 5x + 2) - (x^2 - 5x + 2) =
x^2 - 5x + 2/3x^5 -15x^4 +4x^3 +11x^2 -9x +2
- 3x^5 -15x^4 +6x^3
- 2x^3 +11x^2 -9x +2
- 2x^3 +10x^2 -4x
x^2 -5x +2 x^2/x^2 = 1
- x^2 -5x +2
0 1 (x^2 - 5x + 2) = x^2 - 5x + 2
Since the degree of the remainder is less than the degree of the divisor, then were done:
Therefore, 3x^5 - 15x^4 + 4x^3 + 11x^2 - 9x + 2/x^2 - 5x + 2
= 3x^3 - 2x + 1
+ 0
x^2 - 5x + 2 = 3x^3 - 2x + 1
Answer:
3x^5 - 15x^4 + 4x^3 + 11x^2 - 9x + 2/x^2 - 5x + 2
= 3x^3 - 2x + 1
+ 0
x^2 - 5x + 2
Answer: Letter Choice (A), (3x^3 - 2x + 1)
Hope that helps!!!! Have a great night : ) Answer: Letter Choice (A), (3x^3 - 2x + 1)
82): You are Correct Letter Choice (A), is the answer:
V = (L)(W)(H)
5 (x - 2)(x + 3) = 120
x^2 + x - 6 = 24
x^2 + x - 30 = 0
(x + 6)(x - 5) = 0
x = - 6
5 rejected length is negative
x = 5
W = 3in
H = 8in
Your answer: Letter Choice (A), Width 3in, and Height 8in.
Hope that helps!!!! Have a great evening: : )
