Question

question 1 (5 points)
factor the polynomial: \\(x^3 + x^2 - 4x - 4\\)

a) \\((x - 2)^2(x + 1)\\)
b) \\((x + 2)(x - 2)(x + 1)\\)
c) \\((x^2 + 1)(x - 4)\\)
d) \\((x + 2)^2(x + 1)\\)

question 2 (5 points)
what are the real solutions to the equation \\(5x^2 + 29x + 20 = 0\\)?

a) \\(x = -5, x = -4/5\\)
b) \\(x = -4/5, x = 5\\)
c) \\(x = 4/5, x = 5\\)
d) \\(x = -5, x = 4/5\\)

Explanation:

Factor by grouping

Using the Factoring Cubic Polynomials knowledge point

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Factor the difference of squares

Using the Difference of Squares Factoring knowledge point

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Identify the quadratic coefficients

To solve the equation \(5x^2 + 29x + 20 = 0\), we identify the coefficients for the quadratic formula:

$$ a = 5, \quad b = 29, \quad c = 20 $$

Apply the quadratic formula

Using the Quadratic Formula knowledge point

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Calculate the real solutions

Using the Quadratic Formula knowledge point

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Answer:

Question 1

• A) \((x - 2)^2(x + 1)\)
• B) \((x + 2)(x - 2)(x + 1)\) (Correct answer)
• C) \((x^2 + 1)(x - 4)\)
• D) \((x + 2)^2(x + 1)\)

Question 2

• A) \(x = -5, x = -4/5\) (Correct answer)
• B) \(x = -4/5, x = 5\)
• C) \(x = 4/5, x = 5\)
• D) \(x = -5, x = 4/5\)