Question

Factor 1-3

1. X to the second power -14x+45

2.X to the second power -15x+36

3.X to the second power -7x-44

Answer 1

1.
`x^2 - 14x + 45`

You need two numbers that multiply to 45 and add to -14.
Since the numbers must multiply to a positive number, 45, they must both be positive or both be negative. Since they must add to -14, they must both be negative.


`-9 * (-5) = 45`

`-9 + (-5) = -14`

The numbers are -9 and -5.


`x^2 - 14x + 45 = (x - 9)(x - 5)`

2.
`x^2 - 15x + 36`

You need two numbers that multiply to 36 and add to -15.
Since the numbers must multiply to a positive number, 36, they must both be positive or both be negative. Since they must add to -15, they must both be negative.


`-12 * (-3) = 36`

`-12 + (-3) = -15`

The numbers are -12 and -3.


`x^2 - 15x + 36 = (x - 12)(x - 3)`

3.
`x^2 - 7x - 44`

You need two numbers that multiply to -44 and add to -7.
Since the numbers must multiply to a negative number, -44, one number is positive, and one number is negative.


`-11 * 4 = -44`

`-11 + 4 = -7`

The numbers are -11 and 4.


`x^2 - 7x - 44 = (x - 11)(x + 4)`

Solve by factoring:
1.
`x^2 - 15x + 50 = 0`


`(x - 10)(x - 5) = 0`


`x - 10 = 0` or
`x - 5 = 0`


`x = 10` or
`x = 5`

2.
`x^2 = -2x + 15`


`x^2 + 2x - 15 = 0`


`(x - 3)(x + 5) = 0`


`x - 3 = 0` or
`x + 5 = 0`


`x = 3` or
`x + 5 = 0`


`x = 3` or
`x = -5`