Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) · Q(x) + R(x).

Question

P(x) = 3x³ − 7x² − 3x,    D(x) = 3x − 7

P(x) = ?

Please help I keep getting these wrong and I am very confused.

Answer 1

Hey! Lets solve this shall we ?

So, we must find the quotient and remainder of P and put it into P(x) = D(x)*Q(x) + R(x) form. So, we perform long division in this case such that

x² - 1 = Q(x)

D(x) =3x - 7 |-----------------------------------

3x³ - 7x² - 3x

-(3x³ - 7x²)

------------------------

-3x

-(-3x+7)

---------------

-7 = R(x)

Then, we have P(x) = (3x-7)(x²-1) - 7

I hope this helped!