How do you factor #4x^2+25#?

2 Answers
Sep 19, 2016

Answer:

The sum of two squares cannot be factored.

Explanation:

This expression can be described as the Sum of Two Squares.

#4x^2 +25# It cannot be factored with Real numbers

Only the difference of Two Squares can be factored.
#4x^2 -25 = (x+5)(x-5)#

Sep 19, 2016

Answer:

#4x^2+25=(2x-5i)(2x+5i)#

Explanation:

The kind of factors or roots, a quadratic function #ax^2+bx+c#, depends critically on the discriminant #b^2-4ac#.

If the discriminant is #0#, we have equal roots. If it is square of a rational number, roots or factors are rational (provided #a# and #b# are rational). If discriminant is just positive, factors or roots are real and if discriminant is negative or a complex number, they are complex.

In the given polynomial #4x^2+25#, discriminant is #0^2-4×4×25=0-400=-400#. Hence factors / roots are complex.

We can factorize #4x^2+25# as follows:

#4x^2+25#

= #4x^2-(-25)#

= #(2x)^2-(5i)^2#

= #(2x-5i)(2x+5i)#