## College Algebra (10th Edition)

The coefficient of the term that contains $x^3$ is: $-262,440$
RECALL: The term containing $x^j$ in the expansion of $(x+c)^n$ is: ${n}\choose{n-j}$$c^{n-j}x^j$ Using the formula above, the term containing $x^3$ in the expansion of $(x-3)^{10}$ is: =${10}\choose{10-3}$ $(-3)3^{10-3}x^3$ =${10}\choose{7}$ $(-3)^{7}x^3$ $=\dfrac{10!}{7!3!}\cdot (-2187) \cdot x^3 \\=120\cdot (-2187x^3) \\=-262,440x^3$ (note that $c=-3$) Thus, the coefficient of the term that contains $x^3$ is $-262,440$.