
Jonathan W. answered 11/19/13
Tutor
4.9
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Patient and Knowledgeable Berkeley Grad for Math and Science Tutoring
2| 1 -6 1 24 -20 /* k in a box, coefficients of f(x) */
_____________
1 /* leading coefficient */
2| 1 -6 1 24 -20
___2_________ /* 2·1 */
1 -4 /* 2·1 + (-6) */
___2_________ /* 2·1 */
1 -4 /* 2·1 + (-6) */
2| 1 -6 1 24 -20
___2_-8________ /* 2·(-4) */
1 -4 -7 /* 2·(-4) + 1 */
2| 1 -6 1 24 -20
___2_-8_-14_-20__
1 -4 -7 -10 0 /* remainder is 0, so x – 2 divides f(x), so f(2) = 0 */
___2_-8_-14_-20__
1 -4 -7 -10 0 /* remainder is 0, so x – 2 divides f(x), so f(2) = 0 */
Remainder Theorem: f(k) = remainder from division of f(x) by x − k.