what does common linear factors of to polynomials mean?

Question

if the polynomials x^2-4m+2 and 3x^2-2mx-4 have a common linear factor,find the values of m

Answer 1

If two polynomials are said to share a common linear factor, it means that the same linear expression comes in the factorisation of both polynomials.
Let any polynomial ax^2 + bx + c have x - d as factor. x - d is a factor of some other polynomial px^2 + qx + r. x - d is the common linear factor of both polynomials.
a, b, c, d, p,q and r are all constants.

Answer 2

If x-a is a common factor of x^2-4m+2 and 3x^2-2mx-4 then x-a should devide (x+[4m-2]^1/2)(x-[4m-2]^1/2) so 4m-2 should be a root of 3x^2-2mx-4 then 3[4m-2]-2m([4m-2])-4=0

Answer 3

Let roots of the equation of a,b & b,c
a + b = 4m b + c = 2m/3
ab = 2 bc = -4/3

4 equations 4 unknowns.
Solve equation to get value of m.
(x - b) is common linear factor.

Answer 4

i think it just means if graphed they hit each other at a point which would mean that both linear equations would be true at the same time. which essentially means that both of those equations are true

so just solve x^2-4m+2 = 3x^2-2mx-4

it might have more than 1 value though