Question

Mr Thompson, Please help!

Answer 1

Problem 1

Answer: Choice C) x^2-4

Explanation:

Use the difference of squares rule here.

That rule says (a-b)(a+b) = a^2-b^2

In this case, a = x and b = 2.

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Problem 2

Answer: Choice B) 2x^2+7x+5

Work Shown:

(2x+5)(x+1)

y(x+1) ..... let y = 2x+5

xy+y

x(y) + 1(y)

x(2x+5) + 1(2x+5) ... plug in y = 2x+5

2x^2+5x+2x+5

2x^2+7x+5

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Problem 3

Answer: Choice A)  -x^2-5x+7

Explanation:

The standard form of a quadratic is ax^2+bx+c, where a,b,c are real numbers. In the case of choice A, we have a = -1, b = -5, c = 7.

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Problem 4

Answer: Choice D

Explanation:

Along the top we have three green rectangles. If each of them are of length x, then we have x+x+x = 3x so far. Then adding on a yellow piece of 1 unit leads to 3x+1 as the total horizontal width across the top.

Similarly, along the left side we have 1 green portion and 2 yellow leading to x+2. So this shows why this diagram represents (3x+1)(x+2)

A rectangle must be formed with the smaller pieces glued together. We cannot have any gaps or overlaps. The reason we're aiming for a rectangle is because the area of a rectangle is length*width. Think of (3x+1) as the length and (x+2) as the width.