Remember to use zeros as the coefficients for any degrees that are missing from the polynomial.
5x^2+18x+36, R 12
Practice makes perfect
To divide the given polynomials using synthetic division, we first need to rewrite the dividend so that all of the coefficients are present. Any missing terms should be added to the polynomial with a coefficient of 0.
5x^3+8x^2-60
⇕
5x^3+8x^2+ 0x-60Remember that the general form of the synthetic division divisor must be x-a. Since the given divisor is already written in this form, we are ready to go.
Now we are ready to divide!
rl IR-0.15cm r 2 & |rr 5 &8 &0 &-60
Bring down the first coefficient
rl IR-0.15cm r 2 & |rr 5 &8 &0 &-60 & c 5 & & &
Multiply the coefficient by the divisor
rl IR-0.15cm r 2 & |rr 5 &8 &0 &-60 & 10 & & & c 5&
Add down
rl IR-0.15cm r 2 & |rr 5 &8 &0 &-60 & 10 & & & c 5& 18 &
â–¼
Repeat the process for all of the coefficients
Multiply the coefficient by the divisor
rl IR-0.15cm r 2 & |rr 5 &8 &0 &-60 & 10 & 36& & c 5& 18 &
Add down
rl IR-0.15cm r 2 & |rr 5 &8 &0 &-60 & 10 & 36& & c 5& 18 &36&
The quotient is a polynomial of degree 2, with the above coefficients. The remainder is 12.
Quotient & Remainder
5x^2+18x+36 & 12
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!
