Remember to use zeros as the coefficients for any degrees that are missing from the polynomial.
x^2-1
Practice makes perfect
To divide the given polynomials using synthetic division, all the terms of the dividend must be present.
x^3+5x^2-x-5
Since there are no missing terms, we do not need to rewrite the polynomial.
Remember that the general form of the synthetic division divisor must be x-a. Therefore, we need to rewrite ours a little bit.
x+5 ⇔ x-(-5)
Now we are ready to divide!
rl IR-0.15cm r -5 & |rr 1 &5 &-1 &-5
Bring down the first coefficient
rl IR-0.15cm r -5 & |rr 1 &5 &-1 &-5 & c 1 & & &
Multiply the coefficient by the divisor
rl IR-0.15cm r -5 & |rr 1 & 5 &-1 &-5 & -5 & & & c 1&
Add down
rl IR-0.15cm r -5 & |rr 1 & 5 &-1 &-5 & -5 & & & c 1& 0 &
The quotient is a polynomial of degree 2, with the above coefficients. The remainder is 0.
Quotient & Remainder
x^2-1 & 0
Checking Our Answer
Checking the answer
We can check our answer by multiplying the quotient by the divisor, and then adding the remainder. If the answer equals the dividend, it means our answer is correct. Let's do it!
