i NEED ALGEBRA help !!?

Question

i need to factor 2 problems .. and write the equation of the line that goes through ..

2=squared. i 4got the formula :[


x2 - 4x - 45 and 12x(2) + 16x - 3



write the equation of the line that goes through ( 6, -5 ) and (2,7)

Answer 1

ax^2 + bx + c = a*(x - x1)*(x - x2)

x1 = (-b + sqrt(b^2 - 4ac)) / 2a
x2 = (-b - sqrt(b^2 - 4ac)) / 2a

first problem
a =1
b = -4
c = -45

x1 = (+4 + sqrt(16 - 4*(-45))) / 2 = 9
x2 = (+4 - sqrt(16 - 4*(-45))) / 2 = -5

Factored form
(x - 9)*(x + 5)

second problem
a = 12
b = 16
c = -3

x1 = (-16 + sqrt(256 - 4*12*(-3))) / 24 = 1/6
x2 = (-16 - sqrt(256 - 4*12*(-3))) / 24 = -3/2

factored form
= 12 * (x - 1/6) * (x + 3/2)
= (6x - 1) * (2x + 3)

third problem
straight line through two points
y = m*x + b

two linearly independent equations needed using two points (x1,y1) and (x2,y2)

y1 = m*x1 + b ==> -5 = m*6 + b
y2 = m*x2 + b ==> 7 = m*2 + b

Y = A*B

Y = [y1; y2] = [-5; 7]
A = [x1, 1; x2, 1] = [6, 1; 2, 1]
B = [m, b]

know Y and A, solve for B
B = inv(A)*Y

inv(A) = [1, -1; -x2, x1] / (x1 - x2) = [1, -1; -2, 6] / (6 - 2)
= [1/4, -1/4; -1/2, 3/2]

B = inv(A) * Y = [(-5/4) + (-7/4); (5/2) + (21/2)]
= [-3, 13]

So final equation is
y = m*x + b

m = -3
b = 13

y = -3*x + 13

for x = 6, y = -3*(6) + 13 = -5
for x = 2, y = -3*(2) + 13 = 7
check

Answer 2

(x2 - 4x - 45) I can't do a factor tree on these answers, but two factors of -45 that when you add them together you get -4. -9 and 5.

(x-9) (x+5)

Set (x-9) and (x+5) equal to zero, in other words, just change their signs.

x=9 x=-5

12x(2) + 16x - 3 Sorry, I don't remember how to do this problem. =(