Question

Factor the polynomial: 81x^{3}-3

Polynomial factorization
ANSWERED
asked 2021-03-29
Factor the polynomial:
\(\displaystyle{81}{x}^{{{3}}}-{3}\)

Answers (1)

2021-03-31
Step 1
Given,
\(\displaystyle{81}{x}^{{{3}}}-{3}\)
Step 2
On simplification, we get
\(\displaystyle{81}{x}^{{{3}}}-{3}={3}{\left({27}{x}^{{{3}}}-{1}\right)}\)
\(\displaystyle={3}{\left[{\left({3}{x}\right)}^{{{3}}}-{1}^{{{3}}}\right]}\)
\(\displaystyle={3}{\left({3}{x}-{1}\right)}{\left[{\left({3}{x}\right)}^{{{2}}}+{\left({3}{x}\right)}{\left({1}\right)}+{\left({1}\right)}^{{{2}}}\right]}{\left[\because{a}^{{{3}}}-{b}^{{{3}}}={\left({a}-{b}\right)}{\left({a}^{{{2}}}+{a}{b}+{b}^{{{2}}}\right)}\right]}\)
\(\displaystyle={3}{\left({3}{x}-{1}\right)}{\left({9}{x}^{{{2}}}+{3}{x}+{1}\right)}\)
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