Factor each of the following polynomials completely. Indicate any that are not factorable using integers.3x^4-48

Tyra 2021-09-14 Answered
Factor each of the following polynomials completely. Indicate any that are not factorable using integers.
\(\displaystyle{3}{x}^{{4}}-{48}\)

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Expert Answer

Talisha
Answered 2021-09-15 Author has 12904 answers
Consider the following polynomials:
\(\displaystyle{3}{x}^{{4}}-{48}\)
To factorize the polynomials:
\(\displaystyle{3}{x}^{{4}}-{48}={3}{\left({x}^{{4}}-{16}\right)}\)
\(\displaystyle={3}{\left({\left({x}^{{2}}\right)}^{{2}}-{\left({4}\right)}^{{2}}\right)}\)
\(\displaystyle={3}{\left({x}^{{2}}+{4}\right)}{\left({x}^{{2}}-{4}\right)}\) since \(\displaystyle{a}^{{2}}\)
\(\displaystyle-{b}^{{2}}={\left({a}+{b}\right)}{\left({a}-{b}\right)}\)
\(\displaystyle={3}{\left({x}^{{2}}+{4}\right)}{\left({x}^{{2}}-{\left({2}\right)}^{{2}}\right)}\)
\(\displaystyle={3}{\left({x}^{{2}}+{4}\right)}{\left({x}+{2}\right)}{\left({x}-{2}\right)}\)
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