Find the greatest common factor of (a^2+10a+25) and (a^2+25)
You asked:
Find the polynomial greatest common divisor of the following expressions: \(a^{2} + 10 a + 25\), \(a^{2} + 25\)
MathBot Answer:
The greatest common divisor is \(1\).
Begin by factoring all expressions completely. $$\begin{aligned}a^{2} + 10 a + 25 &= \left(a + 5\right)^{2}\\a^{2} + 25 &= a^{2} + 25\\\end{aligned}$$
Find the greatest common divisor by multiplying common factors together, including only the lowest power of those factors which are common to all expressions. \[\operatorname{gcd}(a^{2} + 10 a + 25, a^{2} + 25) = = 1\]