Question
Find the following product:
$\left(x^2-3 x+7\right)(2 x+3)$
$\left(x^2-3 x+7\right)(2 x+3)$
✓
Answer
By column method:
$\ \ \ \ \ \ \text{x}^2-3\text{x}+7\\ \underline{\ \ \ \ \ \ \ \ \ \times(2\text{x}+3)\ \ \ }\\ \ \ \ \ 2\text{x}^3-6\text{x}^2+14\text{x}\\\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\text{x}^2-9\text{x}+21}\\ \ \ \ \ 2\text{x}^3-3\text{x}^2+5\text{x}+21$
$\therefore(\text{x}^2-3\text{x}+7)(2\text{x}+3)$
$=2\text{x}^3-3\text{x}^2+5\text{x}+21$
$\ \ \ \ \ \ \text{x}^2-3\text{x}+7\\ \underline{\ \ \ \ \ \ \ \ \ \times(2\text{x}+3)\ \ \ }\\ \ \ \ \ 2\text{x}^3-6\text{x}^2+14\text{x}\\\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\text{x}^2-9\text{x}+21}\\ \ \ \ \ 2\text{x}^3-3\text{x}^2+5\text{x}+21$
$\therefore(\text{x}^2-3\text{x}+7)(2\text{x}+3)$
$=2\text{x}^3-3\text{x}^2+5\text{x}+21$
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