How do you factor #x^2 + 2x +3#?

Answer 1

Eva Abramson

There are no integer factors for this expression.

There are no integers which are factors.

We would need factors of 3 which add up to 2. There are simply none.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email

Answer 2

Abigail Allen

#x^2+2x+3=(x+1+isqrt2)(x+1-isqrt2)#

Zeros of #ax^2+bx+c# are given by quadratic formula #(-b+-sqrt(b^2-4ac))/(2a)#, however, such a quadratic function can be factorized, if the discriminant #(b^2-4ac)# is square of a rational number.

In #x^2+2x+3#, discriminant is #2^2-4*1*3=4-12=-8# and hence negative. So its zeros are two complex conjugate numbers given by quadratic formula i.e.

#(-2+-sqrt(2^2-4*1*3))/2# or

#(-2+-sqrt(-8))/2# or

#-1+-isqrt2# i.e. #-1-isqrt2# and #-1+isqrt2#

Now, if #alpha# and #beta# are zeros of quadratic polynomial, then its factors are #(x-alpha)(x-beta)#

Hence factors of #x^2+2x+3# are #(x+1+isqrt2)# and #(x+1-isqrt2)# and

#x^2+2x+3=(x+1+isqrt2)(x+1-isqrt2)#

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email

Answer 3

Kennedy Adams

To factor the quadratic expression $x^2 + 2x + 3$ , you look for two numbers that multiply to the constant term (3) and add up to the coefficient of the linear term (2). Since there are no such two numbers, the quadratic expression $x^2 + 2x + 3$ cannot be factored using real numbers. Therefore, it remains in its factored form as $x^2 + 2x + 3$ .

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.