Question

Multiply the polynomials (x-7)(x^2+3x-3)

A. x^3-4x^2-24x+21
B. x^3-7x^2-24x+21
C. x^3-4x^2-3x+21
D. x^3-7x^2-3x+21

Answer 1

`\bf (x-7)(x^2+3x-3)~\hfill \begin{array}{cll} x^2+3x-3\\ * x\\ \cline{1-1} x^3+3x^2-3x \end{array}~~+~~ \begin{array}{cll} x^2+3x-3\\ * -7\\ \cline{1-1} -7x^2-21x+21 \end{array}~\hfill \\\\[-0.35em] ~\dotfill\\\\ (x^3+3x^2-3x) +(-7x^2-21x+21)\implies x^3-4x^2-24x+21`

notice that all you do is simply multiply the terms of either one by the terms of the other sequentially, then add like-terms.