Question
Find the following product: $\left(x^2-5 x+8\right)\left(x^2+2\right)$
✓
Answer
By column method:
$\text{x}^2-5\text{x}+8\\ \underline{ \ \ \times(\text{x}^2+2)\ \ \ \ \ \ }\\\text{x}^4-5\text{x}^3+8\text{x}^2\\\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\text{x}^2-10\text{x}+16}\\\text{x}^4-5\text{x}^3+10\text{x}^2-10\text{x}+16$
$\therefore(\text{x}^2-5\text{x}+8)(\text{x}^2+2)$
$=\text{x}^4-5\text{x}^3+10\text{x}^2-10\text{x}+16$
$\text{x}^2-5\text{x}+8\\ \underline{ \ \ \times(\text{x}^2+2)\ \ \ \ \ \ }\\\text{x}^4-5\text{x}^3+8\text{x}^2\\\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\text{x}^2-10\text{x}+16}\\\text{x}^4-5\text{x}^3+10\text{x}^2-10\text{x}+16$
$\therefore(\text{x}^2-5\text{x}+8)(\text{x}^2+2)$
$=\text{x}^4-5\text{x}^3+10\text{x}^2-10\text{x}+16$
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