All the coefficients in the dividend must be present. Any missing terms should be added to the polynomial with a coefficient of 0.
2
Practice makes perfect
We want to use synthetic division and the Remainder Theorem to find P(a). Let's recall what the Remainder Theorem says.
If you divide a polynomialP(x) of degree n≥ 1
byx-a,then the remainder isP(a).To divide polynomials using synthetic division, all the terms of the dividend must be present. Since there are no missing terms, we do not need to rewrite the polynomial.
x^3-4x^2+2x+3
Now we are ready to divide!
rl IR-0.15cm r 1 & |rr 1 &-4 &2 &3
Bring down the first coefficient
rl IR-0.15cm r 1 & |rr 1 &-4 &2 &3 & c 1 & & &
Multiply the coefficient by the divisor
rl IR-0.15cm r 1 & |rr 1 &-4 &2 &3 & 1 & & & c 1 & & &
Add down
rl IR-0.15cm r 1 & |rr 1 &-4 &2 &3 & 1 & & & c 1 &-3 & &
