Question

2 multiple answer 10 points select all solutions to the equation (2x - 4)(x + 5) = 0. \\(\square\\) \\(x = -\frac{1}{2}\\) \\(\square\\) \\(x = \frac{1}{2}\\) \\(\square\\) \\(x = -2\\) \\(\square\\) \\(x = 2\\) \\(\square\\) \\(x = -5\\) \\(\square\\) \\(x = 5\\) 3 multiple choice 10 points which expression is equivalent to (3x - 1)(x + 5)? \\(\bigcirc\\) \\(x^2 + 4x - 5\\) \\(\bigcirc\\) \\(3x^2 - 5\\) \\(\bigcirc\\) \\(3x^2 + 4x - 5\\) \\(\bigcirc\\) \\(3x^2 + 14x - 5\\)

Explanation:

For Question 2:

Step1: Set first factor to 0

$2x - 4 = 0$

Step2: Solve for x

$2x=4 \implies x=2$

Step3: Set second factor to 0

$x + 5 = 0$

Step4: Solve for x

$x=-5$

Step1: Apply distributive property (FOIL)

$(3x-1)(x+5)=3x\cdot x + 3x\cdot5 -1\cdot x -1\cdot5$

Step2: Simplify each term

$=3x^2 +15x -x -5$

Step3: Combine like terms

$=3x^2 +14x -5$

Answer:

$x=2$, $x=-5$

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For Question 3: