How do you factor x^2 + 5x + 6?

4 Answers
Jun 20, 2018

See a solution process below:

Explanation:

Because the x^2 coefficient is 1 we know the coefficient for the x terms in the factor will also be 1:

(x )(x )

Because the constant is a positive and the coefficient for the x term is also positive we know the sign for the constants in the factors will both be positive.

(x + )(x + )

Now we need to determine the factors which multiply to 6 and also add to 5:

1 xx 6 = 6; 1 + 6 = 7 <- this is not the factor

2 xx 3 = 6; 2 + 3 = 5 <- this IS the factor

(x + 2)(x + 3)

Jun 20, 2018

Factorize of polynomial x^2+5x+6 = (x+2)*(x+3)

Explanation:

x^2 + (a+b)x + ab = (x+a)*(x+b)

x^2+5x+6 = (x+a)*(x+b)

Equation system:
1. a+b = 5
2. ab = 6
Then a = 2 and b=3

Jun 20, 2018

(x+3)(x+2)

Explanation:

color(purple)("First Answer:")

Using prime factorization of 6

+6=2xx3=1xx6=-2xx-3=-1xx-6

since the coefficient of x is positive

color(red)("the answers "-2xx-3 " and " -1xx-6 " are refused ")

color(blue)("and the answers "2xx3 " and " 1xx6 " are accepted ")

and then we try adding the two numbers to get the coefficient of x

1+6=7rarrcolor(red)("refused")

2+3=5rarrcolor(blue)("accepted")

so it will be

x^2+5x+6=(x+2)(x+3)

color(purple)("The Second Answer")

if you have a polynomial function
color(blue)(ax^2+bx+c=0

the solution set will be

color(green)(x=(-bcolor(red)(+-)sqrt(b^2-4ac))/(2a)

and using it like this

a(x-(-bcolor(red)(+)sqrt(b^2-4ac))/(2a))(x-(-bcolor(red)(-)sqrt(b^2-4ac))/(2a))

so for your question

x^2+5x+6

a=1,b=5,c=6

x=(-5+-sqrt(25-4xx1xx6))/(2xx1)=(-5+-1)/2

and by using it in the formula

1*(x-(-5+1)/2)(x-(-5-1)/2)

=(x+2)(x+3)

Jun 20, 2018

(x+2)(x+3)

Explanation:

The key realization is that we need to think of two numbers that add up to the middle term, and have a product of the middle term.

What two numbers sum up to 5 and have a product of 6?

After some trial and error, we arrive at 2 and 3, because

2+3=5 (Middle term) and

2*3=6 (Last term)

These will be our factors. So we can write our expression as

(x+2)(x+3)

Hope this helps!