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

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

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Talisha
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 $$\displaystyle{a}^{{2}}$$
$$\displaystyle-{b}^{{2}}={\left({a}+{b}\right)}{\left({a}-{b}\right)}$$
$$\displaystyle={3}{\left({x}^{{2}}+{4}\right)}{\left({x}^{{2}}-{\left({2}\right)}^{{2}}\right)}$$
$$\displaystyle={3}{\left({x}^{{2}}+{4}\right)}{\left({x}+{2}\right)}{\left({x}-{2}\right)}$$