Question

question 13 (5 points)
subtract: \\((4x^3 + 9xy + 8y) - (3x^3 + 5xy - 8y)\\)
a) \\(7x^3 + 14xy\\)
b) \\(x^3 + 4xy + 16y\\)
c) \\(x^3 + 4xy\\)
d) \\(7x^3 + 14xy + 16y\\)

question 14 (5 points)
which of the following is not a factor of \\(x^3 - 3x^2 - 4x + 12\\)?
a) \\((x - 2)\\)
b) \\((x + 3)\\)
c) \\((x + 2)\\)
d) \\((x - 3)\\)

question 15 (5 points)
use pascals triangle to find the coefficients of the expanded polynomial \\((a + b)^3\\).
a) 1 3 3 1
b) 1 2 1
c) 1 4 6 4 1
d) 1 1

Explanation:

Distribute the negative sign

Using the Simplifying Algebraic Expressions knowledge point

$$ -(3x^2 + 5xy - 8y) = -3x^2 - 5xy + 8y $$

Combine like terms

Using the Simplifying Algebraic Expressions knowledge point

$$
LATEXBLOCK0
$$

Test factors using remainder theorem

Using the Polynomial Remainder Theorem knowledge point

$$
LATEXBLOCK1
$$

Identify Pascal's triangle row

To expand a binomial to the power of \(n\), we look at row \(n\) of Pascal's triangle (starting with row 0 for \(n=0\)).
For \((a+b)^3\), the exponent is \(n=3\).
The rows of Pascal's triangle are:

• Row 0: 1
• Row 1: 1 1
• Row 2: 1 2 1
• Row 3: 1 3 3 1

Thus, the coefficients for \((a+b)^3\) are 1, 3, 3, 1.

Answer:

Question 13

• A) \(7x^2 + 14xy\)
• B) \(x^2 + 4xy + 16y\) (Correct answer)
• C) \(x^2 + 4xy\)
• D) \(7x^2 + 14xy + 16y\)

Question 14

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

Question 15

• A) 1 3 3 1 (Correct answer)
• B) 1 2 1
• C) 1 4 6 4 1
• D) 1 1