Use synthetic division

Question

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)

Answer 1

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|  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 */

 

Remainder Theorem:  f(k) = remainder from division of f(x) by x − k.