Can someone check my answers for the following problems.

Question

Simplify. Assume that no denominator equals 0.
1)(7x^2+3x-9)-(-x^2+8x-3)
answer: 6x^2-5x-6

2) 5x^3(7x)^2
answer: 245x^5

3) (2x-3)^2
answer: 4x^2-9

4) Use synthetic division to find (2x^3-5x^2+7x-1)/(x-1)
answer: 3

5)Identify the vertex,axis of symmetry, and direction of opening for y=2(x+3)^2-5
answer:
Axis of symmetry is x= -3/4
vertex -3/4
opens up

6) write y=-4x^2+8x-1 in vertex form
answer: (-4x+4)^2-17

Answer 1

1)(7x^2+3x-9)-(-x^2+8x-3)
answer: 6x^2-5x-6
now wait a minute
7 x^2 - ( -x^2) = 7 x^2 + x^2 = 8 x^2
agree with -5x-6

3) (2x-3)^2
answer: 4x^2-9
NO
(2x-3)(2x-3) = 4x^2-12 x + 9

now if you factor 4x^2 - 9 you get (2x-3)(2x+3)

Answer 2

4) Use synthetic division to find (2x^3-5x^2+7x-1)/(x-1)
answer: 3
Well I get a remainder of 3
2x^2 - 3 x + 4 and remainder of 3

Answer 3

5)Identify the vertex,axis of symmetry, and direction of opening for y=2(x+3)^2-5
answer:
Axis of symmetry is x= -3/4
vertex -3/4
opens up
===============
yes, opens up because as |x| gets big, y gets big +
(x+3) = 0 at x = -3
That is axis of symmetry
when x = -3
y = -5
so vertex at (-3,-5)

Answer 4

6) write y=-4x^2+8x-1 in vertex form
answer: (-4x+4)^2-17

y+1 = -4 x^2 + 8 x
-(y+1)/4 = x^2 - 2x
complete square by adding (-2/2)^2 to both sides
-(y+1)/4 + 1 = x^2 -2 x +1
-(y+1)/4 + 1 = (x-1)^2
(x-1)^2 = -y/4 -1/4 +4/4
(x-1)^2 = (-1/4)(y-3)
vertex (1,+3)

Answer 5

For #1-3 I have to simplify them...and for #1 would it be 8x^2-5x-6 in the book it tells me to use the FOIL method.

Answer 6

and for #1 would it be 8x^2-5x-6
Yes

3) (2x-3)^2
answer: 4x^2-9

NO
(2x-3)(2x-3) = 4x^2-12 x + 9 <--- That is FOIL