Answer:
-50xy and -40x²
Step-by-step explanation:
1) Common factor of the letters: x, x², and x³.
It is the common letter with the lowest exponent: x
2) Common factors of the coefficients (numbers): 36, 22, and 144
i) prime factors of 36: 36 = 2² × 3²
ii) prime factors of 22: 22 = 2 × 11
iii) prime factors of 144: 2⁴ × 3²
iv) Greatest common factor: the repeated number raised to the lowest power: 2.
3) Therefore, the greatest common factor of the terms 36x³ - 22x² - 144x is 2x
4) Any number that has 2x as a factor will not change this common factor.
5) Factors of the choices:
i) –11: 2x is not a factor of - 11, therefore this does not apply
ii) –50xy: 2x is a factor, since - 50xy / (2x) = - 25y, therefore this applies.
iii) –40x²: 2x is a factor, since - 40x² / (2x) = -20x, therefore this applies
iv) 24: 2x is not factor of 24, therefore this does not apply
v) 10y: 2x is not a factor of 10y, therefore this does not apply
