how to factor x^2 + 5x +6 ?

Question

Can someone show me how to do it in detail...

Answer 1

look for two numbers that multiply to 6 and add up to 5

2 and 3

(x+2)(x+3)

hope this helps.

Answer 2

Copmpleting the square

x² + 5x + 6 = 0

x² + 5x + 6 - 6 = 0 - 6

x² + 5x = - 6

x² + 5x + _____ = - 6 + _____

x² + 5x + 25/4 = - 6 + 25/4

(x + 5/2)(x + 5/2) = - 24/4 + 25/4

(x - 5/2)² = 1/4

(√x + 5/2)² = ± √1 / √4

x + 5/2 = ± 1/2

x + 5/2 - 5/2 = - 5/2 ± 1/2

x = - 5/2 ± 1/2

- - - - - - - - - - -

Solving for +

x = - 5/2 + 1/2

x = - 4/2

x = - 2

- - - - - -

Solving for -

x = - 5/2 - 1/2

x = - 6/2

x = - 3

- - - - - - - - - -

Method 2

x² + 5x + 6

find the sum of the middle term

x = 1

Multiply the first term times 6

1 x 6 = 6

Factors of 6 = 1, 2, 3, 6

2 + 3 satisft the sum of the middle term

x² + 3x + 2x + 6

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

(x + 2)(x + 3)

- - - - - - - -

Roots

X + 2 = 0

x = 2 - 2 = 0 - 2

x = - 2

- - - - - - - -

Roots

x + 3 = 0

x + 3 - 3 = 0 - 3

x = - 3

-- - - - - - - -

Quadratic formula

x = - b ± √b² - 4ac / 2a

also works
- - - - - - - - - - -s-

Answer 3

First, set the equation equal to 0: x^2+5x+6=0
Next, find all the factors of 6: (1,6) (-1,-6) (2,3) (-2,-3)
Then, find the two factors that add up to 5: (2,3)
Then factor it out: (x+2)(x+3)=0
Set each answer equal to 0: (x+2=0) (x+3=0)
Solve for x: (x=-2) (x=-3)

Hope that helps!

~queenpan1295

Answer 4

Answer is (x + 3).(x + 2)
Only one way to obtain x² term and this is x times x
Need two numbers that multiply to give 6 and add to give 5. These numbers are 3 and 2.

Check
x times x = x²
x times 2 = 2x
3 times x = 3x
3x + 2x = 5x
3 times 2 = 6

Answer 5

use the quadratic equation to find the values of x to give a solution of 0, then solve (x + a), (x + b) for each =0. (the quadratic equation gives you the results as pr above [-2, -3], which is why you have to solve for a and b - in effect, change the sign of x for a and b - to give you the factors rather than the solution for f(x)=0)).

quadratic equation: [-b +/- (b^2 - 4ac)^1/2] / (2a) with a=1, b=5, c=6 gives you -2, -3 as solutions for x where f(x)= 0.

Answer 6

Well, they say that the best way to remember how to factor is remember the phrase "I AM" which stands for "I Add Multiply" meaning that you need to find 2 numbers that add to the B (middle number) and multiply to the C (3rd number)... the numbers 2 and 3 add to 5 and when multiplied = 6, so therefore you result with (X+3)(X+2)

Answer 7

(x+3)(x+2)
write all the factors of 6
and the pair when added will give you +5 are your constant factors
the factors of x^2 are x and x

Answer 8

x^2 + 5x + 6.
2 numbers that you can mutiply
together to get 6 that add up to 5.

y= (x+2)(x+3)
then use the FOIL Method.
F- First
O- outside
I- Inside
L- last
to get.
y= x^2+2x+3x+6
y= x^2+5x+6

Answer 9

If you try (x+2)*(x+3),
then you get x^2 + 5x + 6.
Cheers,
-Shaojun

Answer 10

x^2+5x+6=0
x^2+2x+3x+6=0
x(x+2)+3(x+2)=0
(x+2)(x+3)=0
x+2=0,x+3=0
x= -2, x= -3