Question

x^2-5x+6 and x^3-6x^2+11x+a have a common factor. Find the value of a

Answer 1

factorise the polynomial
${x}^{2} - 5x + 6$
one of the zero satisfied the another polynomial according to the question
${x}^{2} - 3x - 2x + 6 = 0 \\ x(x - 3) - 2(x - 3) = 0 \\ (x - 3)(x - 2) = 0 \\ x = 3 \\ x = 2$
out of these two values ,one satisfies the another,so let put the value 3 in it
27-54+33+a=0
6+a=0
a = -6 ans