Question

PLEASE HELP ASAP!!!

Simplify the following expression.

(x+1)^2-3(x+2)

a. x^2-3x+7
b. x^2-x-5
c. x^2-3x-5
d. x^2-x+3


Simplify the following expression.

(5x^3y^-3)(-6x^4y)

a. -30x^7y^2
b. -30x^12y^3
c. -30x^12/y^3
d. -30x^7/y^2


Solve the following equation.

8+x/2 - x+3/3=4

a. x=-14
b. x=6
c. x=14
d. x=-6


Solve the equation.

x^2-3x-8=x+4

a. x=-6 or x=2
b. x=1+ sqrt5 or x=1- sqrt5
c. x=1+2sqrt3 or x=1-2sqrt3
d. x=-2 or x=6


Joseph is solving the equation x^2+8x-4=0 using the technique completing the square.
x^2+8x-4=0
x^2+8x+?=4+?
What number should Joseph add to both sides of the equation to complete the square, and why?


a. He should add 4 to both sides because 8/2=4.
b. He should add 4 to both sides because (4/2)^2=4.
c. He should add 16 to both sides because 16/2=8.
d. He should add 16 to both sides because (8/2)^2=16.

Answer 1

Explanation:

1) x² - x - 5 (B)

2) -30x⁷/y² (D)

3) x=6 (B)

4)x = 6 and -2 (D)

5) (8/2)² = 16 (D)

Answer 2

1. (x+1)²-3(x+2)
= x² + 2x + 1 - 3x - 6
= x² - x - 5 (the answer is B)

2. (5x³y⁻³)(-6x⁴y)
= -30x³⁺⁴y⁻³⁺¹
= -30x⁷y⁻²
= -30x⁷/y² (the answer is D)

3. [(8+x)/2 - (x+3)/3=4]*6
3(8+x) - 2(x+3) = 24
24 + 3x - 2x - 6 = 24
x = 24 - 24 +6
x=6 (the answer is B)

4. x²-3x-8=x+4
x² - 3x - x -8 - 4 = 0
x² - 4x -12 = 0
(x-6)(x+2) = 0
x = 6 and -2 ( the answer is D)

5. To complete the squares, divide the middle term by two and find its square. That would be (8/2)² = 16. The answer is D.