Factor theorem states,
"If a polynomial p(x) is divided by (x - a) and the remainder after the division is zero, (x - a) will be a factor of the polynomial."
And we can represent it algebraically as,
p(x) = (x - a)q(x)
Here, q(x) is the quotient.
Now we will divide the given polynomial (6x⁵ - 22x² + 11x - 126) by (x - 2).
x - 2) 6x⁵ + 0.x⁴ + 0.x³ + 22x² + 11x - 126 (6x⁴+ 12x³+ 24x²+ 70x + 2
6x⁵ - 12x⁴
-------------------
12x⁴ + 0.x³
12x⁴ - 24x³
--------------------
24x³ + 22x²
24x³ - 48x²
---------------------------
70x² + 11x
70x² - 52x
--------------------------
63x - 126
63x - 126
------------------------
0
Since, remainder of the division is zero,
Therefore, (x - 2) is a factor of the given polynomial.
learn more of factor theorem here brainly.com/question/18575355
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