can someone please solve this for me by using synthetic division and write it in steps [tex]x ^{4}+2x ^{3}-10 x^{2}-18x+9=0 [/tex]
Accepted Solution
A:
If you don't want to test random numbers to see what reduces the polynomial to 0, you can try applying the rational root theorem to narrow down the possible choices. The RRT says that the polynomial *may* have rational roots determined by the leading and constant coefficients.
Factors of constant term: [tex]\pm1,\pm3,\pm9[/tex] Factors of leading term's coefficient: [tex]\pm1[/tex] Possible rational roots: [tex]\pm1,\pm3,\pm9[/tex] (i.e. divide all factors of constants terms by all factors of leading coefficient)
Denoting the given polynomial by [tex]p(x)[/tex], we get