Question

In Exercises use synthetic division to perform the indicated division. Write the polynomial in the form p(x) = d(x)q(x) + r(x)

Answer 1

Answer:

This method is applied for dividing polynomials by binomials of the form $x-k$. These are the steps you must follows:

a) Take the coefficients of $p(x)$ and write them down in order.

b) Copy the leftmost coefficient  to the bottom. Hence the first coefficient of the quotient is the same first coefficient of the dividend.

c) Add terms in vertical patterns and multiply by $k$ in diagonal patterns.

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The figures below show those steps. Thus, we can write the polynomial  p(x) = d(x)q(x) + r(x) in the form:

$\boxed{p(x)=(x-1)(3x+1)+2}$