Factoring functions?

Question

x^2 - 2x - 2400 = 0
= x^2 - 2x +1 - 1 -2400
= (x-1)^2 - 2401
correct?

Answer 1

This is correct as far as it goes, but it's not factoring the function.

Note that 2401 = 49^2, so we have
(x-1)^2 - 49^2
= ((x-1) - 49) . ((x-1) + 49)
= (x - 50) . (x + 48)

Now it has been factored.

Answer 2

x² - 2x - 2400 = 0

Sum of the roots = -b/a = -(-2)/1 = 2
Product of the roots = ac = 1 * -2400 = -2400 where a , b , c are coefficients of the quadratic equation ax²+bx+c = 0

Roots of the quadratic equation =
(-b ± √b² - 4ac )/2a
(-(-2) ± √(-2)² - 4(1)(-2400))/2(1) a = 1 b = -2 and c = -2400
(2± √4+9600)/2
(2± √9604)/2
(2 ± 98)/2
Roots are (2 + 98) /2 and (2 - 98)/2
Roots are 100/2 = 50 and -96/2 = -48
Roots are (50, -48)

To check your answer:
Sum of the roots = 50-48 = 2
Product of the roots = 50 * -48 = -2400

Answer 3

Remember that -2400 is a product of two numbers whose sum in this case is -2
Notice that 48*50=2400
(x-50)(x+48)=xx-2x-2400

Answer 4

yup seems right! using completing the square
but what is your purpose? that form is often used to find the min/ max value for graphing.
this factors properly into 2 brackets
i know this as the discriminant : b^2 -4*a*c= a square number


x^2 - 2x - 2400 = 0
( x+ )(x-)=0
then use the zero property

Answer 5

x^ -- 2x -- 2400
= x^2 -- 50x + 48x -- 2400
= x(x -- 50) + 48(x -- 50)
= (x -- 50)(x + 48)