1. [tex] x^2 - 14x + 45 [/tex]
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.
[tex] -9 \times (-5) = 45 [/tex]
[tex] -9 + (-5) = -14 [/tex]
The numbers are -9 and -5.
[tex] x^2 - 14x + 45 = (x - 9)(x - 5) [/tex]
2. [tex] x^2 - 15x + 36 [/tex]
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.
[tex] -12 \times (-3) = 36 [/tex]
[tex] -12 + (-3) = -15 [/tex]
The numbers are -12 and -3.
[tex] x^2 - 15x + 36 = (x - 12)(x - 3) [/tex]
3. [tex] x^2 - 7x - 44 [/tex]
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.
[tex] -11 \times 4 = -44 [/tex]
[tex] -11 + 4 = -7 [/tex]
The numbers are -11 and 4.
[tex] x^2 - 7x - 44 = (x - 11)(x + 4) [/tex]
Solve by factoring:
1. [tex] x^2 - 15x + 50 = 0 [/tex]
[tex] (x - 10)(x - 5) = 0 [/tex]
[tex] x - 10 = 0 [/tex] or [tex] x - 5 = 0 [/tex]
[tex] x = 10 [/tex] or [tex] x = 5 [/tex]
2. [tex] x^2 = -2x + 15 [/tex]
[tex] x^2 + 2x - 15 = 0 [/tex]
[tex] (x - 3)(x + 5) = 0 [/tex]
[tex] x - 3 = 0 [/tex] or [tex] x + 5 = 0 [/tex]
[tex] x = 3 [/tex] or [tex] x + 5 = 0 [/tex]
[tex] x = 3 [/tex] or [tex] x = -5 [/tex]
