ugg math... algebra II to be exact?

Question

how do you do these problems:
by the way *= squared
~factoring monomials first~ (factor the expression)
1) 3x* + 54x + 243
2) 8y* - 28y - 60
3) 112a* - 168a + 63
4) u* + 7u
5) -v* + 2v - 1

Equations in standard form (solve the equation)
1)x* + 9x = -20
2)5p* - 25 = 4p* + 24
3)(w + 6)* = 3(w + 12) - w*

I realize that it's a lot of problems for one question but it you could do one of the first equations and one of the second equations I would really appreciate it. Also do you think you could show me the steps on how to to these. I am so very lost! Please help and thanks! Will choose best answer!!!

Answer 1

Set 1
Question 1
3 x² + 54 x + 243
3 (x ² + 18 x + 81)
3 (x + 9) (x + 9)
3 (x + 9) ²

Question 5
- (v ² - 2v + 1)
- ( v - 1 ) (v - 1 )
- ( v - 1 ) ²

Set 2
Question 1
x ² + 9x + 20 = 0
(x + 5) (x + 4) = 0
x = - 5 , x = - 4

Question 3
w ² + 12w + 36 = 3w + 36 - w ²
2 w ² + 9w = 0
w (2w + 9) = 0
w = 0 , w = - 9/2

Hope these help.

Answer 2

Look for a common factor on all the problems 1-5:
ab + ac = a(b+c) so:
1) 3x* + 54x + 243 = 3(x* + 18x + 81)
Often the trinomial can be factored again.
3(x +9)(x+9) or 3(x+9)^2
Standard form is ax* +bx + c = 0 (all equations will equal zero and the values are arranged in descending order of degree or powers.)
1) x* +9x +20 =0
2)p* -49 = 0

Answer 3

1)

3x^2 + 54x + 243

=>3(x^2 + 18x + 81)

=>3(x+9)^2

2)

8y^2 - 28y - 60

4(2y^2 - 7y - 15)

4(2y^2 - 10y + 3y - 15)

4(2y(y - 5) + 3(y - 5))

4(y-5)(2y+3)

3)

112a^2 - 168a + 63

=>7(16a^2 - 24a+ 9)

=>7(16a^2 - 12a - 12a + 9)

=>7[4a(4a - 3)- 3(4a - 3)]

=>7(4a-3)(4a-3) or 7(4a-3)^2

4)

u^2 + 7u = u(u+7)

5)

-v^2 + 2v - 1

-(v^2 - 2v + 1)

-(v - 1)^2

6)

x^2 + 9x = -20

x^2 + 9x + 20 = 0

(x +5)(x + 4) = 0

x = -5 or - 4

7)

5p^2 - 25 = 4p^2 + 24

p^2-49 = 0

(p+7)(p-7) = 0

p = 7 or -7

8)

(w+6)^2 = 3(w + 12) - w^2

=>w^2 + 12w + 36 = 3w + 36 - w^2

=>2w^2 + 9w = 0

=>w(2w + 9) = 0

w = 0 or -9/2

Answer 4

The courses I took from 7th grade on are as follows: 7th: Pre-algebra/Algebra I 8th: Plane-solid-coordinate Geometry 9th- Algebra II/Trigonometry 10th- Precalculus Errr, and that's it so far. Take the course you think you can handle best. I'd say most people take either Trig or Precalc after Algebra II.

Answer 5

1)x* + 9x = -20
=> 1)x^2 + 9x +20 = 0
=> ( x+5)( x+4 ) = 0
=> x = -5 OR x= -4

QED