Question

1. find the lcm of the pair of polynomials. $2x^2 - 18$ and $5x^3 + 30x^2 + 45x$ $10x(x + 3)(x - 3)$ $10x(x + 3)^2(x - 3)$ $(x + 3)^2(x - 3)$ $(x - 3)^2(x + 3)$

Explanation:

Step1: Factor first polynomial

2x² - 18 = 2(x² - 9) = 2(x + 3)(x - 3)

Step2: Factor second polynomial

5x³ + 30x² + 45x = 5x(x² + 6x + 9) = 5x(x + 3)²

Step3: Find LCM of factors

LCM = 2×5×x×(x + 3)²×(x - 3) = 10x(x + 3)²(x - 3)

Answer:

10x(x + 3)²(x - 3)