# Thread: LCM and HCF of Algebric Expressions

1. ## LCM and HCF of Algebric Expressions

,
What is the method to find the LCM and HCF of the following expressions?
$x^3 - 2x^2 - 13x -10$ and $x^3 - x^2 -10x - 8$

2. $P(x)=x^3 - x^2 -10x - 8 \ and \ Q(x)=x^3 - 2x^2 - 13x -10$
$factors\ of\ P(x) =(x+1)(x+2)(x+4)$
$factors\ of\ Q(x) =(x+1)(x+2)(x-5)$
$common\ factors\ of\ P(x)\ and\ Q(x) = (x+1),(x+2),(x+1)(x+2)$

Highest Common Factors (HCF) of P(x) and Q(x) $=(x+1)(x+2)$

$since \ (LCM)\ of \ P(x) \ and \ Q(x)= \frac{P(x) \times Q(x)}{HCF}$

$\ LCM =\frac{(x+1)(x+2)(x+4) \times (x+1)(x+2)(x-5)}{(x+1)(x+2)}$

$Least\ common\ multiplier\ (LCM)\ of\ P(x)\ and\ Q(x)=(x+1)(x+2)(x+4)(x-5)$

3. Originally Posted by saberteeth
,
What is the method to find the LCM and HCF of the following expressions?
$x^3 - 2x^2 - 13x -10$ and $x^3 - x^2 -10x - 8$
Factor each, and then make a table with the factors:

[HTML]P(x): (x + 1)(x + 2)(x + 4)
Q(x): (x + 1)(x + 2) (x - 5)
----------------------------------
LCM: (x + 1)(x + 2)(x + 4)(x - 5)
HCF: (x + 1)(x + 2)[/HTML]
The LCM is the product of all the factors; the HCF (or GCF, for Americans) is the product of only the common factors.

4. Originally Posted by ramiee2010
$P(x)=x^3 - x^2 -10x - 8 \ and \ Q(x)=x^3 - 2x^2 - 13x -10$
$factors\ of\ P(x) =(x+1)(x+2)(x+4)$
$factors\ of\ Q(x) =(x+1)(x+2)(x-5)$
$common\ factors\ of\ P(x)\ and\ Q(x) = (x+1),(x+2),(x+1)(x+2)$

Highest Common Factors (HCF) of P(x) and Q(x) $=(x+1)(x+2)$

$since \ (LCM)\ of \ P(x) \ and \ Q(x)= \frac{P(x) \times Q(x)}{HCF}$

$\ LCM =\frac{(x+1)(x+2)(x+4) \times (x+1)(x+2)(x-5)}{(x+1)(x+2)}$

$Least\ common\ multiplier\ (LCM)\ of\ P(x)\ and\ Q(x)=(x+1)(x+2)(x+4)(x-5)$
Thanks, i got it. But, how did you find the factors so accurately? What method did you use?

5. Originally Posted by saberteeth
...how did you find the factors so accurately? What method did you use?
To learn how to factor polynomials, try here.

6. Cool. Just what i needed.