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Popular Pre Algebra >

lcm x^2-x-6,x^2+5x+6

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Solution

lcm

Solution

(x+2)(x+3)(x−3)
Solution steps
Find Least Common Multiplier of x2−x−6,x2+5x+6
Factor x2−x−6:(x+2)(x−3)
x2−x−6
Break the expression into groups
x2−x−6
Definition
Factors of 6:1,2,3,6
6
Divisors (Factors)
Find the Prime factors of 6:2,3
6
6divides by 26=3⋅2=2⋅3
2,3 are all prime numbers, therefore no further factorization is possible=2⋅3
Add the prime factors: 2,3
Add 1 and the number 6 itself1,6
The factors of 61,2,3,6
Negative factors of 6:−1,−2,−3,−6
Multiply the factors by −1 to get the negative factors−1,−2,−3,−6
For every two factors such that u∗v=−6,check if u+v=−1
Check u=1,v=−6:u∗v=−6,u+v=−5⇒FalseCheck u=2,v=−3:u∗v=−6,u+v=−1⇒True
u=2,v=−3
Group into (ax2+ux)+(vx+c)(x2+2x)+(−3x−6)
=(x2+2x)+(−3x−6)
Factor out xfrom x2+2x:x(x+2)
x2+2x
Apply exponent rule: ab+c=abacx2=xx=xx+2x
Factor out common term x=x(x+2)
Factor out −3from −3x−6:−3(x+2)
−3x−6
Rewrite 6 as 3⋅2=−3x−3⋅2
Factor out common term −3=−3(x+2)
=x(x+2)−3(x+2)
Factor out common term x+2=(x+2)(x−3)
Factor x2+5x+6:(x+2)(x+3)
x2+5x+6
Break the expression into groups
x2+5x+6
Definition
Factors of 6:1,2,3,6
6
Divisors (Factors)
Find the Prime factors of 6:2,3
6
6divides by 26=3⋅2=2⋅3
2,3 are all prime numbers, therefore no further factorization is possible=2⋅3
Add the prime factors: 2,3
Add 1 and the number 6 itself1,6
The factors of 61,2,3,6
For every two factors such that u∗v=6,check if u+v=5
Check u=1,v=6:u∗v=6,u+v=7⇒FalseCheck u=2,v=3:u∗v=6,u+v=5⇒True
u=2,v=3
Group into (ax2+ux)+(vx+c)(x2+2x)+(3x+6)
=(x2+2x)+(3x+6)
Factor out xfrom x2+2x:x(x+2)
x2+2x
Apply exponent rule: ab+c=abacx2=xx=xx+2x
Factor out common term x=x(x+2)
Factor out 3from 3x+6:3(x+2)
3x+6
Rewrite 6 as 3⋅2=3x+3⋅2
Factor out common term 3=3(x+2)
=x(x+2)+3(x+2)
Factor out common term x+2=(x+2)(x+3)
Multiply each factor with the highest power:(x+2)⋅(x+3)⋅(x−3)

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Frequently Asked Questions (FAQ)

  • What is lcm x^2-x-6,x^2+5x+6 ?

    The solution to lcm x^2-x-6,x^2+5x+6 is (x+2)(x+3)(x-3)

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