To find the additional linear factors of a polynomial when one factor is given, you can use long division or synthetic division. Since the factor x - 3 is given, we can use synthetic division to find the quotient.
Using synthetic division, we set up the problem as follows:
3 | 1 -6 11 -6
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| 3 -9 6
|___________________
1 -3 2 0
The remainder is 0, and the coefficients of the quotient are 1, -3, and 2.
Therefore, the quotient is x^2 - 3x + 2.
The additional linear factors of the polynomial x^3 - 6x^2 + 11x - 6 are the solutions to the quadratic equation x^2 - 3x + 2 = 0.
To factor the quadratic equation, we find the roots by factoring:
(x - 2)(x - 1) = 0
So, the additional linear factors are:
(x - 2)(x - 1)
Therefore, the correct answer is c. (x-2)(x-1).
What are the additional linear factors of x^3−6x^2+11x−6 if x−3 is a factor? (1 point)
a. (x-2)(x+1)
b. (x+2)(x-1)
c. (x-2)(x-1)
d. (x+2)(x+1)
1 answer