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.
===========================================================
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
===========================================================
Problem 3
Answer: Choice A) -x^2-5x+7
Step-by-step 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.
===========================================================
Problem 4
Answer: Choice D
Step-by-step 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.