What is the GCD of x²-3x-10, x²-10x+25?
You asked:
Find the polynomial greatest common divisor of the following expressions: \(x^{2} - 3 x - 10\), \(x^{2} - 10 x + 25\)
MathBot Answer:
The greatest common divisor is \(x - 5\).
Begin by factoring all expressions completely. $$\begin{aligned}x^{2} - 3 x - 10 &= \left(x - 5\right) \left(x + 2\right)\\x^{2} - 10 x + 25 &= \left(x - 5\right)^{2}\\\end{aligned}$$
Find the greatest common divisor by multiplying common factors together, including only the lowest power of those factors which are common to all expressions. \[\operatorname{gcd}(x^{2} - 3 x - 10, x^{2} - 10 x + 25) = (x - 5)^{1} = x - 5\]