Question:
Find the product:
(x3 − 5x2 + 3x + 1) × (x3 − 3)
Solution:
By horizontal method:
$\left(x^{3}-5 x^{2}+3 x+1\right) \times\left(x^{2}-3\right)$
$=x^{2}\left(x^{3}-5 x^{2}+3 x+1\right)-3\left(x^{3}-5 x^{2}+3 x+1\right)$
$=x^{5}-5 x^{4}+3 x^{3}+x^{2}-3 x^{3}+15 x^{2}-9 x-3$
$=x^{5}-5 x^{4}+16 x^{2}-9 x-3$
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