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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Popular >

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

Solution

lcm

x^{2} - x - 6, x^{2} + 5 x + 6

Solution

(x + 2) (x + 3) (x - 3)

Solution steps

Find Least Common Multiplier of

x^{2} - x - 6, x^{2} + 5 x + 6

Factor

x^{2} - x - 6 : (x + 2) (x - 3)

x^{2} - x - 6

Break the expression into groups

x^{2} - x - 6

Definition

Factors of

6 : 1, 2, 3, 6

6

Divisors (Factors)

Find the Prime factors of

6 : 2, 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

Add the prime factors:

2, 3

Add 1 and the number

6

itself

1, 6

The factors of

6

1, 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 \Rightarrow

FalseCheck

u = 2, v = - 3 : u * v = - 6, u + v = - 1 \Rightarrow

True

u = 2, v = - 3

Group into

(a x^{2} + ux) + (vx + c)

(x^{2} + 2 x) + (- 3 x - 6)

= (x^{2} + 2 x) + (- 3 x - 6)

Factor out

x

from

x^{2} + 2 x : x (x + 2)

x^{2} + 2 x

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

x^{2} = xx

= xx + 2 x

Factor out common term

x

= x (x + 2)

Factor out

- 3

from

- 3 x - 6 : - 3 (x + 2)

- 3 x - 6

Rewrite

6

3 \cdot 2

= - 3 x - 3 \cdot 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

x^{2} + 5 x + 6 : (x + 2) (x + 3)

x^{2} + 5 x + 6

Break the expression into groups

x^{2} + 5 x + 6

Definition

Factors of

6 : 1, 2, 3, 6

6

Divisors (Factors)

Find the Prime factors of

6 : 2, 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

Add the prime factors:

2, 3

Add 1 and the number

6

itself

1, 6

The factors of

6

1, 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 \Rightarrow

FalseCheck

u = 2, v = 3 : u * v = 6, u + v = 5 \Rightarrow

True

u = 2, v = 3

Group into

(a x^{2} + ux) + (vx + c)

(x^{2} + 2 x) + (3 x + 6)

= (x^{2} + 2 x) + (3 x + 6)

Factor out

x

from

x^{2} + 2 x : x (x + 2)

x^{2} + 2 x

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

x^{2} = xx

= xx + 2 x

Factor out common term

x

= x (x + 2)

Factor out

3

from

3 x + 6 : 3 (x + 2)

3 x + 6

Rewrite

6

3 \cdot 2

= 3 x + 3 \cdot 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) \cdot (x + 3) \cdot (x - 3)

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2 \cdot 3^{2}

longdivision 8/12 long division

\frac{8}{12}

3^2*(-2)^3

3^{2} \cdot (- 2)^{3}

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\frac{64}{16}

8^3-9*2/3

8^{3} - 9 \cdot \frac{2}{3}

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)