# LCM and HCF of Algebric Expressions

• Oct 6th 2009, 04:07 AM
saberteeth
LCM and HCF of Algebric Expressions
(Hi),
What is the method to find the LCM and HCF of the following expressions?
$\displaystyle x^3 - 2x^2 - 13x -10$ and $\displaystyle x^3 - x^2 -10x - 8$
• Oct 6th 2009, 05:01 AM
ramiee2010
$\displaystyle P(x)=x^3 - x^2 -10x - 8 \ and \ Q(x)=x^3 - 2x^2 - 13x -10$
$\displaystyle factors\ of\ P(x) =(x+1)(x+2)(x+4)$
$\displaystyle factors\ of\ Q(x) =(x+1)(x+2)(x-5)$
$\displaystyle common\ factors\ of\ P(x)\ and\ Q(x) = (x+1),(x+2),(x+1)(x+2)$

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

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

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

$\displaystyle Least\ common\ multiplier\ (LCM)\ of\ P(x)\ and\ Q(x)=(x+1)(x+2)(x+4)(x-5)$
• Oct 6th 2009, 06:39 AM
stapel
Quote:

Originally Posted by saberteeth
(Hi),
What is the method to find the LCM and HCF of the following expressions?
$\displaystyle x^3 - 2x^2 - 13x -10$ and $\displaystyle x^3 - x^2 -10x - 8$

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. (Wink)
• Oct 7th 2009, 02:59 AM
saberteeth
Quote:

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

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

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

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

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

Thanks, i got it. But, how did you find the factors so accurately? What method did you use?
• Oct 7th 2009, 07:47 AM
stapel
Quote:

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. (Wink)
• Oct 7th 2009, 10:14 AM
saberteeth
Cool. Just what i needed.