Question

(2x + 1)(3x² + x - 4) = ......
a. 5x³ + 5x² - 5x - 3
b. 6x³ + 5x² - 7x - 4
c. 11x² - 7x - 4
d. 6x³ + 3x² + 4x - 4
type in the letter of the correct choice: a, b, c or d

question 9 1 pts
(x + 7)² = ____ (hint: expand this out)
a. x² + 7x + 14
b. x² + 14x + 49
c. 2x² + x + 49
d. x² + 49
type in the letter of the correct choice: a, b, c or d

Explanation:

First Question:

Step1: Expand the product

Using the distributive property (FOIL for polynomials), we multiply \(2x\) by each term in \(3x^2 + x - 4\) and then \(1\) by each term in \(3x^2 + x - 4\).
\(2x(3x^2)+2x(x)+2x(-4)+1(3x^2)+1(x)+1(-4)\)

Step2: Simplify each term

\(6x^3 + 2x^2 - 8x + 3x^2 + x - 4\)

Step3: Combine like terms

Combine the \(x^2\) terms (\(2x^2 + 3x^2 = 5x^2\)) and the \(x\) terms (\(-8x + x = -7x\)).
\(6x^3 + 5x^2 - 7x - 4\)

Step1: Recall the formula for squaring a binomial

The formula \((a + b)^2 = a^2 + 2ab + b^2\). Here, \(a = x\) and \(b = 7\).

Step2: Apply the formula

\(x^2 + 2(x)(7) + 7^2\)

Step3: Simplify the terms

\(x^2 + 14x + 49\)

Answer:

B

Second Question: