Marya wants to factor the polynomial 36x3 – 22x2 – 144x. Which term can she add to the polynomial that would not change its greatest common factor? Check all that apply. –11 –50xy –40x2 24 10y

Answer: -50xy and -40x²Explanation:1) Common factor of the letters: x, x², and x³.It is the common letter with the lowest exponent: x2) Common factors of the coefficients (numbers): 36, 22, and 144i) prime factors of 36: 36 = 2² × 3²ii) prime factors of 22: 22 = 2 × 11iii) prime factors of 144: 2⁴ × 3²iv) 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 2x4) 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 applyii) –50xy: 2x is a factor, since - 50xy / (2x) = - 25y, therefore this applies.iii) –40x²: 2x is a factor, since - 40x² / (2x) = -20x, therefore this appliesiv) 24: 2x is not factor of 24, therefore this does not applyv) 10y: 2x is not a factor of 10y, therefore this does not apply.