Question

use synthetic division to perform \\((x^4 - 3x + 5) \div (x - 4)\\).

a) \\(x^3 + 4x^2 + 16x + 61 - \frac{249}{x - 4}\\)
b) \\(x^3 - 4x^2 + 16x + 61 + \frac{249}{x - 4}\\)
c) \\(x^3 + 4x^2 + 16x + 61 + \frac{249}{x - 4}\\)
d) \\(x^3 - 4x^2 + 16x + 61 - \frac{249}{x - 4}\\)

question 7 (5 points)
use synthetic division to find the remainder if polynomial \\(p(x) = x^3 - 28x - 48\\) is divided by \\(x + 4\\).

a) 0
b) 1
c) 3
d) 2

question 8 (5 points)
which of the following shows the factorization of \\(3x^4 + 6x^3 + 4x^2 + 8x\\)?

a) \\(x(3x^2 + 4)(x + 2)\\)
b) \\((3x^2 + 4)(x + 2)\\)
c) \\(x(3x + 4)(x + 2)\\)
d) \\(x(3x^2 + 4)(x - 2)\\)

Explanation:

Perform synthetic division for the first question

$$
LATEXBLOCK0
$$

$$ (x^4 - 3x + 5) \div (x - 4) = x^3 + 4x^2 + 16x + 61 + \frac{249}{x - 4} $$

Find the remainder for Question 7

$$ P(-4) = (-4)^3 - 28(-4) - 48 = -64 + 112 - 48 = 0 $$

Factor the polynomial in Question 8

$$
LATEXBLOCK1
$$

Answer:

Question 1

• A) \(x^3 + 4x^2 + 16x + 61 - 249 / x - 4\)
• B) \(x^3 - 4x^2 + 16x + 61 + 249 / x - 4\)
• C) \(x^3 + 4x^2 + 16x + 61 + 249 / x - 4\) (Correct answer)
• D) \(x^3 - 4x^2 + 16x + 61 - 249 / x - 4\)

Question 7

• A) 0 (Correct answer)
• B) 1
• C) 3
• D) 2

Question 8

• A) \(x(3x^2 + 4)(x + 2)\) (Correct answer)
• B) \((3x^2 + 4)(x + 2)\)
• C) \(x(3x + 4)(x + 2)\)
• D) \(x(3x^2 + 4)(x - 2)\)