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.
2x^5-6x^4-2x^2+7x-4
⇕
2x^5-6x^4+ 0x^3-2x^2+7x-4
Remember 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.
The quotient is a polynomial of degree 4, with the above coefficients. The remainder is - 1.
Quotient & Remainder
2x^4-2x+1 & - 1
We can see the above to rewrite the given expression.
(2x^5-6x^4-2x^2+7x-4) ÷ (x-3)
⇕
2x^4-2x+1+- 1/x-3
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!
