Use synthetic division to decide whether k=2, k=-1, or k=0 are zeros of
f(x)=x^4-6x^3+x^2+24x-20. If not, give the value of f(k)
f(x)=x^4-6x^3+x^2+24x-20. If not, give the value of f(k)
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.