Final answer:
To determine if x-3 is a factor of a quadratic expression, substitute x=3 into the expression and check if it evaluates to zero.
Step-by-step explanation:
To determine whether x-3 is a factor of 6x²+4x+34, we need to check if x-3 divides evenly into the given quadratic expression. To do this, we can use the Remainder Theorem. If the expression evaluates to zero when we substitute x=3, then x-3 is a factor. Let's check:
Substituting x=3 into the expression:
6(3)²+4(3)+34 = 54+12+34 = 100
The expression evaluates to 100, which is not zero. Therefore, x-3 is not a factor of 6x²+4x+34.