Problem 7
Subtract 4 from both sides to get
3x^2 = 4
3x^2-4 = 0
3x^2 + 0x - 4 = 0
We see that a = 3, b = 0, c = -4
<h3>Answer: Choice B</h3>
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Problem 8
If you were to expand and simplify each item given, then you'll find that choices C and D involve an x^2 term, while choices A and B do not. So we can rule out choices A and B.
We can also rule out choice D since it is not an equation. Rather, it's an inequality. Therefore, only choice C is a quadratic equation.
<h3>Answer: Choice C</h3>
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Problem 9
Let's simplify and get everything to one side
4x(x-2) = 5
4x^2 - 8x = 5
4x^2 - 8x - 5 = 0
It's in the standard form ax^2+bx+c = 0 where
a = 4, b = -8, c = -5
<h3>Answer: Choice A</h3>
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Problem 10
Follow the same idea as problem 9 earlier. You'll need to use the FOIL rule.
3x + (x+5)(2x-3) = 7
3x + 2x^2 - 3x + 10x - 15 = 7
3x + 2x^2 - 3x + 10x - 15 - 7 = 0
2x^2 + 10x - 22 = 0
<h3>Answer: Choice D</h3>